"Use properties of the indefinite integral to express..." was answered by our experts

High School
Calculus and Analysis
Calculus 2
Applications of integrals

hadejada7x

Answered question

2021-12-17

Use properties of the indefinite integral to express the following integral in terms of the simplest integrals:

\int (7 x^{2} - 6 x) d x

Answer & Explanation

Beverly Smith

Beginner2021-12-18Added 42 answers

Step 1
Use the following property of indefinite integral:

\int [f (x) - g (x)] d x = \int f (x) d x - \int g (x) d x

\int k f (x) d x = k \int f (x) d x

Consider the following indefinite integral:

\int (7 x^{2} - 6 x) d x = \int 7 x^{2} d x - \int 6 x d x

= 7 \int x^{2} d x - 6 \int x d x

Step 2
Hence, the simplest form of integral is

7 \int x^{2} d x - 6 \int x d x

Ben Owens

Beginner2021-12-19Added 27 answers

\int (7 x^{2} - 6 x) d x

Lets

nick1337

Expert2021-12-28Added 777 answers

$\int 7 x^{2} - 6 x d x$
Use the property of integral $\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x$
$\int 7 x^{2} d x - \int 6 x d x$
$\frac{7 x^{3}}{3} - \int 6 x d x$
$\frac{7 x^{3}}{3} - 3 x^{2}$
Add the constant of integration
$\frac{7 x^{3}}{3} - 3 x^{2} + C$

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