Micah Haynes

2022-04-04

What is $\int (-3{t}^{4}-t+2)\ufeffdt$?

Ariella Bruce

Beginner2022-04-05Added 19 answers

Remove parentheses.

$\int -3{t}^{4}-t+2dt$

Split the single integral into multiple integrals.

$\int -3{t}^{4}dt+\int -tdt+\int 2dt$

Since $-3$ is constant with respect to $t$, move $-3$ out of the integral.

$-3\int {t}^{4}dt+\int -tdt+\int 2dt$

By the Power Rule, the integral of $t}^{4$ with respect to $t$ is $\frac{1}{5}{t}^{5}$.

$-3(\frac{1}{5}{t}^{5}+C)+\int -tdt+\int 2dt$

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

$-3(\frac{1}{5}{t}^{5}+C)-\int tdt+\int 2dt$

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

$-3(\frac{1}{5}{t}^{5}+C)-(\frac{1}{2}{t}^{2}+C)+\int 2dt$

Apply the constant rule.

$-3(\frac{1}{5}{t}^{5}+C)-(\frac{1}{2}{t}^{2}+C)+2t+C$

Simplify.

$-\frac{3{t}^{5}}{5}-\frac{{t}^{2}}{2}+2t+C$

Reorder terms.

$-\frac{3}{5}{t}^{5}-\frac{1}{2}{t}^{2}+2t+C$

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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