Donald Johnson

2021-12-30

find the indefinite integral and check the result by differentiation.

$\int (x+7)dx$

Raymond Foley

Beginner2021-12-31Added 39 answers

Step 1 Solve the indefinite integral

The integral mentioned in the question is,

$\int (x+7)dx$

Let this indefinite integral be equal to a function y.

Thus,

$y=\int (x+7)dx$

Now, solve the indefinite integral.

$y=\frac{{x}^{2}}{2}+7x$

Step 2 Check the result by differentiation

The solution of the given indefinite integral is obtained as,

$y=\frac{{x}^{2}}{2}+7x$

Differentiate the given function to see whether it gives back the initial integral.

$\frac{dy}{dx}=\frac{1}{2}\frac{d}{dx}\left({x}^{2}\right)+\frac{d}{dx}\left(7x\right)$

$\Rightarrow \frac{dy}{dx}=\frac{1}{2}\left(2x\right)+\left(7\right)$

$\Rightarrow \frac{dy}{dx}=x+7$

This is the same as the initial expression. Thus, the solution to the given initial integral is correct.

The integral mentioned in the question is,

Let this indefinite integral be equal to a function y.

Thus,

Now, solve the indefinite integral.

Step 2 Check the result by differentiation

The solution of the given indefinite integral is obtained as,

Differentiate the given function to see whether it gives back the initial integral.

This is the same as the initial expression. Thus, the solution to the given initial integral is correct.

Edward Patten

Beginner2022-01-01Added 38 answers

It is required to calculate:

$\int (x+7)dx$

Lets

Lets

karton

Expert2022-01-04Added 613 answers

Use properties of integrals

Evaluate the integrals

Add C

Answer:

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