Get the answer to "Solve the following integral ∫043x(4−x)dx=32 ∫04x(x−4)dx"

Phoebe

Answered question

2020-11-12

Solve the following integral

\int_{0}^{4} 3 x (4 - x) d x = 32

\int_{0}^{4} x (x - 4) d x

wheezym

Skilled2020-11-13Added 103 answers

Step 1

\int_{0}^{4} 3 x (4 - x) d x = 32

We have to evaluate.

\int_{0}^{4} x (x - 4) d x

Step 2
We have,

\int_{0}^{4} 3 x (4 - x) d x = 32

...(1)
and

\int_{0}^{4} x (x - 4) d x =

?
Now,

\Rightarrow \int_{0}^{4} 3 x (4 - x) d x = 32

\Rightarrow 3 \int_{0}^{4} x (4 - x) d x = 32

\Rightarrow \int_{0}^{4} x (4 - x) d x = \frac{32}{3}

\Rightarrow \int_{0}^{4} x (- 1) (x - 4) d x = \frac{32}{3}

\Rightarrow - \int_{0}^{4} x (x - 4) d x = \frac{32}{3}

\Rightarrow \int_{0}^{4} x (x - 4) d x = - \frac{32}{3}

Hence,

\int_{0}^{4} x (x - 4) d x = - \frac{32}{3}

Jeffrey Jordon

Expert2021-11-05Added 2605 answers

Answer is given below (on video)

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