If -0-2cos x d x-a- then -0-cos x d x-

The correct option is C know that ∫_0^2a f(x) dx = 2∫_0^a f(x) dx if f(x) = f(2a x), and ∫_0^2a f(x) dx = 0 if f(x) = f(2a x) Here, f(x) = cos x Let a = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Area between x=g(y) and y Axis

If ∫0π/2cos x...

Question

If $\int_{0}^{\frac{π}{2}} cos x d x = a$ , then $\int_{0}^{π} cos x d x =$ .

2 a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C 0.0
We know that
$\int_{0}^{2 a} f (x) d x = 2 \int_{0}^{a} f (x) d x$ if $f (x) = f (2 a - x)$ , and
$\int_{0}^{2 a} f (x) d x = 0$ if $f (x) = - f (2 a - x)$

Here, f(x) = cos x

Let $a = \frac{π}{2}$
$2 a = π$

Now, $f (2 a - x) = cos (π - x) = - cos x$

Thus, $f (2 a - x) = - f (x)$

Thus, $\int_{0}^{π} cos x d x = 0$

Suggest Corrections

Similar questions

Q. If

\int_{0}^{\frac{π}{2}} c o s (x) d x = a t h e n \int_{0}^{π} c o s (x) d x

is equal to -

Q. If

I_{1} = \int_{0}^{π / 2} cos (sin x) d x

;

I_{2} = \int_{0}^{π / 2} sin (cos x) d x

and

I_{3} = \int_{0}^{π / 2} cos x d x

, then

π / 2 \int 0 cos x d x

\int_{0}^{\frac{π}{2}} \frac{cos x d x}{cos x + sin x}

Q. Assertion :

\int_{0}^{π} \sqrt{1 - {sin}^{2} x} d x = 0

. Reason:

\int_{0}^{π} cos x d x = 0.

Join BYJU'S Learning Program

If ∫π20cosx dx=a, then ∫π0cosx dx=.

The correct option is C 0.0We know that ∫2a0f(x) dx=2∫a0f(x) dx if f(x)=f(2a−x), and ∫2a0f(x) dx=0 if f(x)=−f(2a−x) Here, f(x) = cos x Let a=π2 2a=π Now, f(2a−x)=cos(π−x)=−cosx Thus, f(2a−x)=−f(x) Thus, ∫π0cosx dx=0

If $\int_{0}^{\frac{π}{2}} cos x d x = a$ , then $\int_{0}^{π} cos x d x =$ .