logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

Evaluate the following problems using second fundamental theorem: $\int\limits_{1}^{2}\large\frac{dx}{x^{2}+5x+6}$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • If $F(x)=\int \limits_a^x f(t)dt $ then $\int \limits_a^b f(x) dx=F(b)-F(a)$
Given $\int \limits_0^2 \large\frac{dx}{x^2+5x+6}$
Step 1:
$\int \limits_0^2 \large\frac{dx}{x^2+5x+6}$$=\int \limits_0^2 \large\frac{dx}{\bigg(x+\Large\frac{5}{2}\bigg)^2-\frac{25}{4}+6}$
$\qquad=\int \limits_0^2 \large\frac{dx}{\bigg(x+\Large\frac{5}{2}\bigg)^2-\bigg(\frac{1}{2}\bigg)^2}$
Step 2:
$\qquad=\large\frac{1}{2}$$.2 \bigg[\log (x +\large\frac{5}{2} -\frac{1}{2} )-$$\log (x+\large\frac{5}{2}+\frac{1}{2})\bigg]_0^2$
Step 3:
$\qquad=\log (x +2) - \log (x+3)\bigg]_0^2$
$\qquad= \log \bigg(\large\frac{x+2}{x+3}\bigg)\bigg]_0^2$
$\qquad=\log \large\frac{4}{5}$$-\log \large\frac{2}{3}$
$\qquad=\log \large\frac{4}{5}$$ \times \large\frac{3}{2}$
$\qquad=\log \large\frac{6}{5}$
answered Aug 14, 2013 by meena.p
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...