David Young

2021-12-27

Evaluate the definite integral.

${\int}_{1}^{4}(8{x}^{3}-x)dx$

eskalopit

Beginner2021-12-28Added 31 answers

Step 1

Given that ,

The integral${\int}_{1}^{4}(8{x}^{3}-x)dx$

By using integration formulas,

$\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$

$\int cf\left(x\right)dx=c\int f\left(x\right)dx$

$\int (f\left(x\right)-g\left(x\right))dx=\int f\left(x\right)dx-\int g\left(x\right)dx$

Step 2

${\int}_{1}^{4}(8{x}^{3}-x)dx$

$={\int}_{1}^{4}8{x}^{3}dx-{\int}_{1}^{4}xdx$

$=8{\int}_{1}^{4}{x}^{3}dx-{\int}_{1}^{4}xdx$

$=8{\left[\frac{{x}^{4}}{4}\right]}_{1}^{4}-{\left[\frac{{x}^{2}}{2}\right]}_{1}^{4}$

$=2{\left[{x}^{4}\right]}_{1}^{4}-{\left[\frac{{x}^{2}}{2}\right]}_{1}^{4}$

$=2[{4}^{4}-1]-[\frac{{4}^{2}}{2}-\frac{1}{2}]$

$=2[256-1]-[\frac{16}{2}-\frac{1}{2}]$

$=510-\left[\frac{15}{2}\right]$

$=\frac{1005}{2}$

Given that ,

The integral

By using integration formulas,

Step 2

Mary Herrera

Beginner2021-12-29Added 37 answers

Lets

Vasquez

Expert2022-01-08Added 669 answers

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