Compute ∫ 4 7 t 2 cos − 1 ⁡ ( t ) d t.

Question

Compute   ∫      4    7        t          2            cos          −      1        ⁡  (  t  )  d  t.

aushilfem8sif · Accepted Answer

This integral could not be completed using integration by parts. Mathway will use another method.

Simplify.

$\int \frac{4}{7} t^{2} - \cos (t) d t$

Split the single integral into multiple integrals.

$\int \frac{4}{7} t^{2} d t + \int - \cos (t) d t$

Since $\frac{4}{7}$ is constant with respect to $t$ , move $\frac{4}{7}$ out of the integral.

$\frac{4}{7} \int t^{2} d t + \int - \cos (t) d t$

By the Power Rule, the integral of $t^{2}$ with respect to $t$ is $\frac{1}{3} t^{3}$ .

$\frac{4}{7} (\frac{1}{3} t^{3} + C) + \int - \cos (t) d t$

Since $- 1$ is constant with respect to $t$ , move $- 1$ out of the integral.

$\frac{4}{7} (\frac{1}{3} t^{3} + C) - \int \cos (t) d t$

The integral of $\cos (t)$ with respect to $t$ is $\sin (t)$ .

$\frac{4}{7} (\frac{1}{3} t^{3} + C) - (\sin (t) + C)$

Simplify.

$\frac{4}{21} t^{3} - \sin (t) + C$

Compute 4 7 t 2 </mrow> cos − 1