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Recent questions tagged ch7
Questions
$\Large \int\frac{dx}{\sin(x-a)\sin(x-b)}$ is equal to\begin{array}{1 1}(A)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C & (B)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \\(C)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C &(D)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \end{array}
cbse
class12
ch7
q49
p167
objective
exemplar
sec-b
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
$\Large \int\frac{\cos 2x-\cos 2\theta}{\cos x-\cos\theta}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;2(\sin x+x\cos\theta)+C & (B)\;2(\sin x-x\cos\theta)+C\\(C)\;2(\sin x+2x\cos\theta)+C & (D)\;2(\sin x-2x\cos\theta)+C\end{array}
cbse
class12
ch7
q48
p166
objective
exemplar
sec-b
easy
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_ {\Large\frac{-\pi}{4}}^{\Large\frac{\pi}{4}} \log(\sin x+\cos x)dx$
cbse
class12
ch7
q47
p166
exemplar
sec-c
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_0^{\Large \pi} x \log \sin xdx$
cbse
class12
ch7
q46
p166
exemplar
sec-b
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int\limits_0^1 x\;log(1+2x)dx$
cbse
class12
ch7
q45
p166
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_0^{\Large\frac{\pi}{2}}\large\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^2}\quad\normalsize \text{(Hint:Divide Numerator and Denominator by $\cos^4x)$}$
cbse
class12
ch7
q44
p166
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate :$\int \sqrt \tan x \;dx\;$
cbse
class12
ch7
q43
p166
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int e^{-3x}\cos^3xdx$
cbse
class12
ch7
q42
p166
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_{\Large \frac{\pi}{3}}^{\Large \frac{\pi}{2}}\large\frac{\sqrt{1+\cos x}}{(1-\cos x)^{\large\frac{5}{2}}}$
cbse
class12
ch7
q41
p166
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\sin^{-1}\sqrt{\large\frac{x}{a+x}}dx\quad(Hint:Put\;x=a\tan^2\theta)$
cbse
class12
ch7
q40
p166
exemplar
sec-c
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int e^{\tan^{-1}x}\bigg(\frac{1+x+x^2}{1+x^2}\bigg)dx$
cbse
class12
ch7
q39
p166
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\displaystyle\int\frac{2x-1}{(x-1)(x+2)(x-3)}dx$
cbse
class12
ch7
q38
p165
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_0^{\Large\pi} \large \frac{x}{1+\sin x}$
cbse
class12
ch7
q37
p165
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\displaystyle\int\frac{x^2dx}{(x^2+a^2)(x^2+b^2)}$
cbse
class12
ch7
q36
p165
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\displaystyle\int\frac{x^2dx}{x^4-x^2-12}$
cbse
class12
ch7
q35
p165
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int\limits_0^{\Large \frac{1}{2}}\frac{dx}{(1+x^2)\sqrt {1-x^2}}$$(Hint:let\;x=\sin\theta)$
cbse
class12
ch7
q34
p165
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int\limits_0^\pi x\sin x\cos^2xdx$
cbse
class12
ch7
q33
p165
exemplar
sec-c
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int\limits_0^1\frac{xdx}{\sqrt{1+x^2}}$
cbse
class12
ch7
q32
p165
exemplar
sec-a
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_1^2\frac{dx}{\sqrt{(x-1)(2-x)}}$
cbse
class12
ch7
q31
p165
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int\limits_0^{\Large \frac{\pi}{2}}\Large \frac{\tan xdx}{1+m^2\tan^2x}$
cbse
class12
ch7
q30
p165
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int\limits_0^1\frac{dx}{e^x+e^{-x}}$
cbse
class12
ch7
q29
p165
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following as limits of sums: $ \int\limits_0^2e^xdx$
cbse
class12
ch7
q28
p165
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following as limits of sums: $\int\limits_0^2(x^2+3)dx$
cbse
class12
ch7
q27
p165
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\displaystyle\int\frac{dx}{x\sqrt{x^4-1}}\;(Hint:Put\;x^2=\sec\theta)$
cbse
class12
ch7
q26
p165
short-answer
exemplar
sec-a
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\displaystyle\int\frac{\cos x-\cos 2x}{1-\cos x}dx$
cbse
class12
ch7
q25
p165
short-answer
exemplar
sec-a
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\frac{\sqrt x}{\sqrt{a^3-x^3}}dx$
cbse
class12
ch7
q24
p165
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following : $\begin{align*} \int \frac{\sin^6x+\cos^6x}{\sin^2x \cos^2x}dx \end{align*}$
cbse
class12
ch7
q23
p164
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following\[\int\frac{(\cos 5x+\cos 4x)}{1-2\cos 3x}dx\]
cbse
class12
ch7
q22
p164
short-answer
exemplar
math
sec-b
asked
Jan 14, 2013
by
sreemathi.v
0
answers
Evaluate the following $\int\frac{\sin^{-1}x}{(1-x^2)^{\frac{3}{2}}}dx$
cbse
class12
ch7
q21
p164
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\sqrt {2ax-x^2}dx$
cbse
class12
ch7
q20
p164
exemplar
short-answer
sec-a
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following\[\int\frac{x^2}{1-x^4}dx\;put\;x^2=t\]
cbse
class12
ch7
q19
p164
short-answer
exemplar
math
sec-a
asked
Jan 14, 2013
by
sreemathi.v
0
answers
Evaluate the following $\int\frac{x}{x^4-1}dx$
cbse
class12
ch7
q18
p164
exemplar
sec-a
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\sqrt {5-2x+x^2}dx$
cbse
class12
ch7
q17
p164
exemplar
sec-a
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\frac{3x-1}{\sqrt{x^2+9}}dx$
cbse
class12
ch7
q16
p164
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\frac{dt}{\sqrt {3t-2t^2}}$
cbse
class12
ch7
q15
p164
short-answer
exemplar
math
sec-b
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\displaystyle\int\frac{dx}{\sqrt {16-9x^2}}$
cbse
class12
ch7
q14
p164
short-answer
exemplar
sec-a
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\frac{\sqrt{1+ x^2}}{x^4}dx$
cbse
class12
ch7
q13
p164
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\large\int\frac{ x^{\frac{1}{2}}}{1+x^{\frac{3}{4}}}dx$ $(Hint:Put\;x=z^4)$
cbse
class12
ch7
q12
p164
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\sqrt{\frac{a+x}{a-x}}$
cbse
class12
ch7
q11
p164
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\displaystyle\int \large \frac{( x)}{\sqrt x+1}$$dx \quad(Hint:Put\;\sqrt x=z)$
cbse
class12
ch7
q10
p164
short-answer
exemplar
sec-a
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\sqrt{1+\sin x}\;dx$
cbse
class12
ch7
q9
p164
short-answer
exemplar
sec-a
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\frac{(\sin x+\cos x)}{\sqrt {1+\sin 2x}}dx$
cbse
class12
ch7
q8
p164
short-answer
exemplar
sec-a
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\tan^2 x\sec^4 x\;dx$
cbse
class12
ch7
q7
p164
short-answer
exemplar
sec-a
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following$\int\frac{dx}{1+\cos x}$
cbse
class12
ch7
q6
p164
short-answer
exemplar
sec-a
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\large\int\frac{(1+\cos x)}{x+\sin x}dx$
cbse
class12
ch7
q5
p164
short-answer
exemplar
sec-a
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following$\displaystyle\int\frac{e^{6log x}-e^{5log x}}{e^{4log x}-e^{3log x}}$$dx$
cbse
class12
ch7
q4
p163
short-answer
exemplar
sec-a
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $ \displaystyle\int\frac{(x^2+2)}{x+1}dx$
cbse
class12
ch7
q3
p163
short-answer
exemplar
sec-a
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Verify the following $ \large\int\frac{2x+3}{x^2+3x}dx=log \mid x^2+3x\mid+C$
cbse
class12
ch7
q2
p163
short-answer
exemplar
sec-b
easy
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Verify the following$ \int\frac{2x-1}{2x+1}dx=x-log \mid (2x+3)^2\mid+C$
cbse
class12
ch7
q1
p163
exemplar
sec-a
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Find an anti derivative(or integral)of the function by the method of inspection $\sin 2x$
cbse
class12
bookproblem
ch7
sec1
q1
p299
sec-a
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
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