First slide

Evaluation of definite integrals

Question

$\int_{- 2}^{0} (x^{3} + 3 x^{2} + 3 x + 3 + (x + 1) \cos (x + 1)) d x =$

Difficult

A

$- 4$
B

0
C

4
D

6

Solution

$x + 1 = t \to I = \int_{- 1}^{1} (t^{3} + 2 + t \cos t) d t$ $= \int_{- 1}^{1} 2 d t,$ $(∵ t^{3} + t \cos t$ is an odd function)
= 4

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