The value of ∫ limits2-2(x cos x + sin x + 1)dx is

Question

The value of ∫ limits2-2(x cos x + sin x + 1)dx is (A) 2 (B) 0 (C) -2 (D) 4

Tardigrade Admin · Accepted Answer

We know, if f(x) is odd, then ∫ limits-aa f(x) d x=0 ∴ I =∫ limits-22(x cos x+ sin x+1) d x =0+0+∫ limits-22 d x (∵ x cos x and sin x are odd) =[x]-22=4

Q. The value of $- 2 \int 2 (x cos x + sin x + 1) d x$ is

2

0

-2

4

We know, if $f (x)$ is odd, then $- a \int a f (x) d x = 0$
$∴ I = - 2 \int 2 (x cos x + sin x + 1) d x$
$= 0 + 0 + - 2 \int 2 d x$
$(∵ x cos x$ and $sin x$ are odd)
$= [x]_{- 2}^{2} = 4$

Q. The value of −2∫2​(xcosx+sinx+1)dx is

2

0

-2

4

We know, if f(x) is odd, then −a∫a​f(x)dx=0 ∴I=−2∫2​(xcosx+sinx+1)dx =0+0+−2∫2​dx (∵xcosx and sinx are odd) =[x]−22​=4

Q. The value of $- 2 \int 2 (x cos x + sin x + 1) d x$ is

We know, if $f (x)$ is odd, then $- a \int a f (x) d x = 0$
$∴ I = - 2 \int 2 (x cos x + sin x + 1) d x$
$= 0 + 0 + - 2 \int 2 d x$
$(∵ x cos x$ and $sin x$ are odd)
$= [x]_{- 2}^{2} = 4$