What is the integral from sin(x) to cos(x) of t^2 ?

The integral from sin(x) to cos(x) of t^2 is (cos^3(x)-sin^3(x))/3

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integral from sin(x) to cos(x) of t^2

\int_{s i n (x)}^{c o s (x)} t^{2} d t

\frac{cos ^{3} ( x ) - sin ^{3} ( x )}{3}

Solution steps

\int_{s i n (x)}^{c o s (x)} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{s i n (x)}^{c o s (x)}

= [\frac{t ^{3}}{3}]_{s i n (x)}^{c o s (x)}

Compute the boundaries:

\frac{cos ^{3} ( x )}{3} - \frac{sin ^{3} ( x )}{3}

= \frac{cos ^{3} ( x )}{3} - \frac{sin ^{3} ( x )}{3}

Simplify

= \frac{cos ^{3} ( x ) - sin ^{3} ( x )}{3}

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What is the integral from sin(x) to cos(x) of t^2 ?
The integral from sin(x) to cos(x) of t^2 is (cos^3(x)-sin^3(x))/3