If f 1 + x = f 1 - x ∀ x ∈ R , then the value of the integral Ι = ∫ - 7 9 f x f x + f 2 - x d x is

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

If

f (1 + x) = f (1 - x)

(\forall x \in R),

then the value of the integral

Ι = \int_{- 7}^{9} \frac{f (x)}{f (x) + f (2 - x)} d x

is

MathematicsDefinite IntegrationJEE Main

Options:

A $0$
B $2$
C $8$
D $10$

Solution:

1625 Upvotes Verified Answer

The correct answer is:

8

As

f (1 + x) = f (1 - x) \overset{x \to x - 1}{\to} f (x) = f (2 - x)

∴

Using

(a + b - x); 2 Ι = \int_{- 7}^{9} \frac{f (x) + f (2 - x)}{f (2 - x) + f (x)} d x

\Rightarrow Ι = 8

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