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Recent questions tagged definite-integrals-as-limit-of-sum

Evaluate $\displaystyle \lim_{n \rightarrow \infty} \bigg[ \large\frac{1^p + 2^p + 3^p....+ n^p}{n^{p+1}} \bigg ] $, where $p \gt -1$

asked Mar 20, 2014 by balaji.thirumalai

1 answer

$I=\int \limits_0^{\frac{\pi}{2}} \sin ^4 x \cos^2 x dx$ find the value of I

asked Dec 20, 2013 by meena.p

1 answer

$I= \int \limits_0^{\frac{\pi}{6}} \cos ^5 3 \theta . \sin ^3 6 \theta d \theta$ Find the value of I.

asked Dec 20, 2013 by meena.p

1 answer

$ I= \int \limits_0^{\frac{\pi}{2}} \cos ^3 x dx$

asked Dec 20, 2013 by meena.p

1 answer

$I= \int \limits_0^{\frac{\pi}{2}} \sin ^2 x dx $ find the value of I

asked Dec 20, 2013 by meena.p

1 answer

$f'(x) = a \cos x + b \sin x ;\; f'(0)=4;\; f(0)=3;\; f \bigg(\large\frac{\pi}{2}\bigg)$$=5$. Find the value of $\;f(x)\;$?

asked Dec 19, 2013 by meena.p

1 answer

$\int \limits _0^{\omega} \large\frac{x^2}{(x^2+a^2) (x^2+b^2) (x^2+c^2)}$$dx= \large\frac{\pi}{2(a+b)(b+c)(c+a)}$ then find $\int \limits _0^{\omega} \large\frac{dx}{(x^2+4)(x^2+g)}$

asked Dec 17, 2013 by meena.p

1 answer

$\int \limits_1^6 (6-4x) dx \leq 6-5b \;\&\;6 > 1$ Find 'b' value

asked Dec 17, 2013 by meena.p

1 answer

If $g(x) =\large\frac{f(x) +f(-x)}{2}$ defined over $[-3,3]$ and $f(x)=2x^2-4x+1$ then $\int \limits_{-3}^3=?$

asked Dec 17, 2013 by meena.p

1 answer

Integrate: $\int \limits_0^{\large\frac{2}{3}}$$ \large\frac{dx}{4+ 9x^2}$

asked Dec 16, 2013 by meena.p

1 answer

Integrate : $I= \int \limits_1^3 \sqrt {3+x^3}.dx$

asked Dec 16, 2013 by meena.p

1 answer

Integrate $I= \int \limits_0^1 e^{x^2} dx$

asked Dec 16, 2013 by meena.p

1 answer

$\large\frac{d}{dx} \int \limits_{x^2}^{x^3} \bigg(\large\frac {1}{lnt} \bigg)$$dx$

asked Dec 14, 2013 by meena.p

1 answer

$f(x)= \large\frac{e^x}{1+e^x}$ $\;I_1= \int \limits_{f(-a)}^{f(a)} x g[(x) (1-x)].dx;\;I_2= \int \limits_{f(-a)}^{f(a)} x g[(x) (1-x)].dx;$ then $\large\frac{I_1}{I_2}=?$

asked Dec 13, 2013 by meena.p

1 answer

Integrate $I= \int \limits_{-\pi}^{\pi} \large\frac{\cos ^2 x}{1+a^x}$$dx$

asked Dec 13, 2013 by meena.p

1 answer

$y= \int \limits_0^n [x]dx=\large\frac{n(n-1)}{2}$ if $n=2$ then $y=?$

asked Dec 13, 2013 by meena.p

1 answer

Integrate :$\int \limits_0^1 \large\frac{1}{\sqrt {x-(z-x)}} $$dx$

asked Dec 12, 2013 by meena.p

1 answer

Integrate :$\int \limits_3^4 \large\frac{1}{\sqrt {(x-3)(4-x)}} $$dx$

asked Dec 12, 2013 by meena.p

1 answer

Integrate : $\int\limits_0^5 \sqrt {\large\frac{x^3}{5-x}}dx$

asked Dec 12, 2013 by meena.p

1 answer

Integrate $\int \limits_0^3 \sqrt {\large\frac{x}{3-x}}$$dx$

asked Dec 12, 2013 by meena.p

1 answer

Integrate $\int \limits_0^1 x(1-x)^n dx. n \in N$

asked Dec 12, 2013 by meena.p

1 answer

Integrate: $\int \large\frac{2}{3} \frac{e^x \sqrt {e^x-4}}{e^x+g}$$dt$

asked Dec 12, 2013 by meena.p

1 answer

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