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

The integral from pi/2 to x^3 of cos(t) is sin(x^3)-1

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integral from pi/2 to x^3 of cos(t)

\int_{\frac{π}{2}}^{x^{3}} cos (t) d t

sin (x^{3}) - 1

Solution steps

\int_{\frac{π}{2}}^{x^{3}} cos (t) d t

Use the common integral:

\int cos (t) d t = sin (t)

= [sin (t)]_{\frac{π}{2}}^{x^{3}}

Compute the boundaries:

sin (x^{3}) - 1

= sin (x^{3}) - 1

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

\int_{1}^{10} \frac{2}{81} x (x - 1) d x

\int_{- 2}^{0} e^{x} (x^{2} + 1) d x

\int_{2}^{5} 2 - 5 x d x

\int_{0}^{1} - sin (\frac{nπ x}{2}) d x

What is the integral from pi/2 to x^3 of cos(t) ?
The integral from pi/2 to x^3 of cos(t) is sin(x^3)-1