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

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

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

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

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

Solution steps

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

Apply the Power Rule

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

= [\frac{x ^{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}

\int_{0}^{\frac{π}{2}} x cos (x) d x

\int_{1}^{3} \frac{ln ( x )}{x ^{2}} d x

\int_{0}^{3} 5 x - 8 d x

\int_{5}^{6} x^{2} + x - 14 d x

\int_{0}^{2} x^{\frac{1}{2}} d x

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