∫ - a a a - x a + x d x =, a π 2, 1, 2 aπ, aπ

I = ∫ - a a a - x a + x d x f ( x ) ⇒ f ( a + b - x ) I = ∫ - a a a + x a - x d x ⇒ 2 I = ∫ - a a 2 a a 2 - x 2 d x I = 2 a ∫ 0 a d x a 2 - x 2 = 2 a sin - 1 x a 0 a = 2 a π 2

∫ - a a a - x a + x d x =

Search any question & find its solution

Question: Answered & Verified by Expert

\int_{- a}^{a} \sqrt{\frac{a - x}{a + x}} d x =

MathematicsDefinite IntegrationAP EAMCETAP EAMCET 2020 (23 Sep Shift 1)

Options:

A $\frac{a π}{2}$
B $1$
C $2 aπ$
D $aπ$

Solution:

2669 Upvotes Verified Answer

The correct answer is:

aπ

$I = \int_{- a}^{a} \sqrt{\frac{a - x}{a + x}} d x$

$f (x) \Rightarrow f (a + b - x)$

$I = \int_{- a}^{a} \sqrt{\frac{a + x}{a - x}} d x$

$\Rightarrow 2 I = \int_{- a}^{a} \frac{2 a}{\sqrt{a^{2} - x^{2}}} d x$

$I = 2 a \int_{0}^{a} \frac{d x}{\sqrt{a^{2} - x^{2}}}$

$= 2 a {(\sin^{- 1} \frac{x}{a})}_{0}^{a}$

$= 2 a (\frac{π}{2})$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play