Integrate 191*-1+x^2 from 0 to 3

\int_{0}^{3}\left(191\left(-1\right)+x^2\right)dx

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Answer

$-564$

Step by step solution

Problem

$\int_{0}^{3}\left(191\left(-1\right)+x^2\right)dx$
1

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

$\int_{0}^{3} x^2dx+\int_{0}^{3}-191dx$
2

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

$\int_{0}^{3} x^2dx+\left[-191x\right]_{0}^{3}$
3

Evaluate the definite integral

$\int_{0}^{3} x^2dx-1\cdot 0\left(-191\right)+3\left(-191\right)$
4

Any expression multiplied by $0$ is equal to $0$

$\int_{0}^{3} x^2dx+0+3\left(-191\right)$
5

Multiply $-191$ times $3$

$\int_{0}^{3} x^2dx+0-573$
6

Subtract the values $0$ and $-573$

$\int_{0}^{3} x^2dx-573$
7

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

$\left[\frac{x^{3}}{3}\right]_{0}^{3}-573$
8

Evaluate the definite integral

$-573+\frac{0^{3}}{3}\left(-1\right)+\frac{3^{3}}{3}$
9

Calculate the power

$-573+\frac{0}{3}\left(-1\right)+\frac{27}{3}$
10

Divide $27$ by $3$

$-573+0\left(-1\right)+9$
11

Any expression multiplied by $0$ is equal to $0$

$-573+0+9$
12

Subtract the values $9$ and $-573$

$-564$

Answer

$-564$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.37 seconds

Views:

107