Integrate 7-3x from -1 to 2

\int_{-1}^{2}\left(7-3x\right)dx

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Answer

$\frac{33}{2}$

Step by step solution

Problem

$\int_{-1}^{2}\left(7-3x\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int_{-1}^{2}-3xdx+\int_{-1}^{2}7dx$
2

The integral of a constant is equal to the constant times the integral's variable

$\int_{-1}^{2}-3xdx+\left[7x\right]_{-1}^{2}$
3

Evaluate the definite integral

$\int_{-1}^{2}-3xdx-1\left(-1\right)\cdot 7+2\cdot 7$
4

Multiply $7$ times $2$

$\int_{-1}^{2}-3xdx+7+14$
5

Add the values $14$ and $7$

$\int_{-1}^{2}-3xdx+21$
6

Taking the constant out of the integral

$21-3\int_{-1}^{2} xdx$
7

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$21-3\left[\frac{1}{2}x^2\right]_{-1}^{2}$
8

Evaluate the definite integral

$\left(2^2\cdot 0.5-1\cdot {\left(-1\right)}^2\cdot 0.5\right)\left(-3\right)+21$
9

Multiply $\frac{1}{2}$ times $-1$

$\left({\left(-1\right)}^2\left(-0.5\right)+2^2\cdot 0.5\right)\left(-3\right)+21$
10

Calculate the power

$\left(1\left(-0.5\right)+4\cdot 0.5\right)\left(-3\right)+21$
11

Multiply $\frac{1}{2}$ times $4$

$\left(2-0.5\right)\left(-3\right)+21$
12

Subtract the values $2$ and $-\frac{1}{2}$

$1.5\left(-3\right)+21$
13

Multiply $-3$ times $\frac{3}{2}$

$21-4.5$
14

Subtract the values $21$ and $-\frac{9}{2}$

$\frac{33}{2}$

Answer

$\frac{33}{2}$

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Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.22 seconds

Views:

81