∫ limits-11 (x27 cos x + ex) dx =

Question

∫ limits-11 (x27 cos x + ex) dx =  (A) (2e - 1/e) (B) (e + 1/e) (C) e - (1/e) (D) (1/e)

Tardigrade Admin · Accepted Answer

Let I = ∫ limits-11 (x27 cos x + ex) dx ⇒ : :: I = ∫ limits-11 x27 cos x dx + ∫ limits-11 ex dx Since f(x) = x27 cos x is an odd function. ∴ : :: ∫ limits-aa f(x) dx = 0 So, I = 0 + |ex |-11 = e - (1/e)

Q. $- 1 \int 1 (x^{27} cos x + e^{x}) d x =$

$\frac{2 e - 1}{e}$

$\frac{e + 1}{e}$

$e - \frac{1}{e}$

$\frac{1}{e}$

Let $I = - 1 \int 1 (x^{27} cos x + e^{x}) d x$
$\Rightarrow I = - 1 \int 1 x^{27} cos x d x + - 1 \int 1 e^{x} d x$
Since $f (x) = x^{27} cos x$ is an odd function.
$∴ - a \int a f (x) d x = 0$
So, $I = 0 + ∣ e^{x} ∣_{- 1}^{1} = e - \frac{1}{e}$

Q. −1∫1​(x27cosx+ex)dx=

e2e−1​

ee+1​

e−e1​

e1​