Question-40 \int_{-2}^0\left(x^3+3x^2+3x+3+(x+1)\cos(x+1)\right)\,dx is equal to
A) 6
B) 4
C) -4
D) 0
Answer: B) 4
Explanation
Let I=\int_{-2}^{0}\left[(x+1)^{3}+2+(x+1) \cos (x+1)\right] d x
Let \boldsymbol{x}+\mathbf{1}=\boldsymbol{y}
I=\int_{-1}^{1}\left(y^{3}+y \cos y+2\right) d y=2 \int_{0}^{1} 2 d yBy even-odd property of definite integral
Hence, I=4