What is the integral from 0 to 1+sin(x) of t^2 ?

The integral from 0 to 1+sin(x) of t^2 is ((sin(x)+1)^3)/3

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integral from 0 to 1+sin(x) of t^2

\int_{0}^{1 + s i n (x)} t^{2} d t

\frac{( sin ( x ) + 1 ) ^{3}}{3}

Solution steps

\int_{0}^{1 + s i n (x)} t^{2} d t

Apply the Power Rule

= [\frac{t ^{3}}{3}]_{0}^{1 + s i n (x)}

Compute the boundaries:

\frac{( sin ( x ) + 1 ) ^{3}}{3}

= \frac{( sin ( x ) + 1 ) ^{3}}{3}

What is the integral from 0 to 1+sin(x) of t^2 ?
The integral from 0 to 1+sin(x) of t^2 is ((sin(x)+1)^3)/3