help@askiitians.com

+91-87964 74404

Grade 12Integral Calculus

evaluate the following integral
∫ 1 / sqrt(1 + cos x) dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{1}{\sqrt{1+cosx}}dx$
$I = \int \frac{1}{\sqrt{2cos^{2}\frac{x}{2}}}dx$
$I = \int \frac{1}{\sqrt{2}cos\frac{x}{2}}dx$
$I = \int \frac{sec\frac{x}{2}}{\sqrt{2}}dx$
$I = \int \frac{sec\frac{x}{2}(sec\frac{x}{2}+tan\frac{x}{2})}{\sqrt{2}(sec\frac{x}{2}+cot\frac{x}{2})}dx$
$sec\frac{x}{2}+tan\frac{x}{2} = t$
$\frac{1}{2}(sec\frac{x}{2}tan\frac{x}{2}+sec^{2}\frac{x}{2})dx = dt$
$I = \int \frac{2}{\sqrt{2}t}dt$
$I = \sqrt{2}logt+c$
$I = \sqrt{2}log(sec\frac{x}{2}+tan\frac{x}{2})+c$

The area of a square field is 640000cm².what is its area in hectares

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

integral calculus

1 Answer Available

Last Activity: 4 Years ago

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

integral calculus

1 Answer Available

Last Activity: 4 Years ago

If 4th term of an A.p is zero, show that the 8th term is double the 6th term

integral calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions