Solve this: Q 26 Evaluate : ∫-aaa-xa+xdx - Maths - Integrals

Question

Solve this:
Q 26 Evaluate : ∫ - a a a - x a + x d x

Abhishek Jha · Accepted Answer

Dear Student,
Here is the solution of your asked query:
We have,I=∫-aaa-xa+xdxPutting x=a cos2y⇒dx=-2a sin2y dyWhen x→a, y→0And x→-a, y→π2I=∫π20-2a sin2ya-a cos2ya+a cos2ydy=∫0π22a 2siny cosy1-cos2y1+cos2ydy=∫0π24a siny cosy×tany dy=2a∫0π22sin2y dy=2a∫0π21-cos2ydy=2ay-sin2y20π2=2aπ2-sinπ2-0-0=2aπ2-0=πa
Regards

Solve this: Q.26. Evaluate : ∫ - a a a - x a + x d x

Solve this:
Q.26. Evaluate : $\int_{- a}^{a} \sqrt{\frac{a - x}{a + x}} d x$