The value of the integral\\int_{1} ^{3}((x-2)^{4} \sin ^{3}(x-2)+(x-2)^{2019}+1) d xis

KVPY 2020-21 SB SX Exam Previous Papers

Question : 16 of 120

Marks: +1, -0

The value of the integral

\∫↙{1} ↖{3}((x-2)^{4} \sin ^{3}(x-2)+(x-2)^{2019}+1) d x

Solution:

\∫↙{1} ↖{3}((x-2)^{4} \sin ^{3}(x-2)+(x-2)^{2019}+1) d x

x-2=t \⇒d x=d t

\∫↙{-1} ↖{1}(t^{4} \sin ^{3} t+t^{2019}+1) d t

=∫↙{-1} ↖{1} d t=t]_{-1}^{1}=2

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