Question

What is the value of ∫ 8 x3 dx.

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Answer 1

$\displaystyle \sf{ \int 8 {x}^{3} dx } = 2 {x}^{4} + c$

Given :

The integral

$\displaystyle \sf{ \int 8 {x}^{3} dx }$

To find :

Integrate the integral

Formula :

$\displaystyle \sf{ \int {x}^{n} dx = \frac{ {x}^{n + 1} }{n + 1} + c }$

Solution :

Solution :Step 1 of 2 :

Write down the given Integral

Here the given Integral is

$\displaystyle \sf{ \int 8 {x}^{3} dx }$

Step 2 of 2 :

Integrate the integral

$\displaystyle \sf{ \int 8 {x}^{3} dx }$

$\displaystyle \sf{ = 8 \int {x}^{3} dx }$

$\displaystyle \sf{ = 8 \times \frac{ {x}^{3 + 1} }{3 + 1} + c \: \: }\: \: \: \bigg[ \: \because \:\int {x}^{n} dx = \frac{ {x}^{n + 1} }{n + 1} + c \: \bigg]$

$\displaystyle \sf{ = 8 \times \frac{ {x}^{4} }{4} + c \: \: }$

$\displaystyle \sf{ = 2 {x}^{4} + c \: \: }$

Where c is integration constant

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