Resolved: "Calculate the integral. ∫(x2−3x+2)dx"

High School
Calculus and Analysis
Calculus 2
Applications of integrals

chezmarylou1i

Answered question

2021-12-29

Calculate the integral.

\int (x^{2} - 3 x + 2) d x

Answer & Explanation

turtletalk75

Beginner2021-12-30Added 29 answers

Step 1

\int (x^{2} - 3 x + 2) d x

The integral is
Since the integration is indefinite; a constant of integration is to be added.
Step 2
Solve the integral.

\int (x^{2} - 3 x + 2) d x = \int x^{2} d x - \int 3 x d x + 2 \int d x

= \frac{x^{2} + 1}{2 + 1} - 3 \cdot \frac{x^{1 + 1}}{1 + 1} + 2 \cdot \frac{x^{0 + 1}}{0 + 1} + C

= \frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x + C

Hence the integral is solved.

Jenny Bolton

Beginner2021-12-31Added 32 answers

\int (x^{2} - 3 x + 2) d x

= \int x^{2} d x - 3 \int x d x + 2 \int 1 d x

\int x^{2} d x

= \frac{x^{3}}{3}

\int x d x

= \frac{x^{2}}{2}

\int 1 d x

\int x^{2} d x - 3 \int x d x + 2 \int 1 d x

= \frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x

\int (x^{2} - 3 x + 2) d x

= \frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x + C

= \frac{x (2 x^{2} - 9 x + 12)}{6} + C

Vasquez

Expert2022-01-07Added 669 answers

Given:
$\int x^{2} - 3 x + 2 d x$
Use rules
$\int x^{2} d x - \int 3 x d x + \int 2 d x$
Evaluate
$\frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x$
Add $C \in R$
Solution:
$\frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x + C, C \in R$

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