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Engineering Mathematics Miscellaneous

Engineering Mathematics

  1. The value of the integral
    20
    (x - 1)² sin(x - 1)
    dx is
    (x - 1)² + cos(x - 1)
    1. 3
    2. 0
    3. –1
    4. –2
Correct Option: B

Let I =
²∫0(x - 1)² sin(x - 1)
dx
(x - 1)² + cos(x - 1)²

We know that, ²∫0
(2 - x - 1)² sin(2 - x - 1)
dx
(2 - x - 1)² + cos(2 - x - 1)²

= - ²∫0
(x - 1)² sin(x - 1)
dx = - 1
(x - 1)² + cos(x - 1)²

⇒ I + I = 0
⇒ 2I = 0
⇒ I = 0



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