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# Evaluate the following integrals. \int (2x^{3}-x^{2}+3x-7)dx

Question
Applications of integrals
asked 2020-11-08
Evaluate the following integrals.
$$\displaystyle\int{\left({2}{x}^{{{3}}}-{x}^{{{2}}}+{3}{x}-{7}\right)}{\left.{d}{x}\right.}$$

## Answers (1)

2020-11-09
Step 1
To evaluate the given integrals.
Step 2
Given that
$$\displaystyle=\int{\left({2}{x}^{{{3}}}-{x}^{{{2}}}+{3}{x}-{7}\right)}{\left.{d}{x}\right.}$$
$$\displaystyle=\int{2}{x}^{{{3}}}{\left.{d}{x}\right.}-\int{x}^{{{2}}}{\left.{d}{x}\right.}+\int{3}{x}{\left.{d}{x}\right.}-\int{7}{\left.{d}{x}\right.}$$
$$\displaystyle={\frac{{{2}{x}^{{{4}}}}}{{{4}}}}-{\frac{{{x}^{{{3}}}}}{{{3}}}}+{\frac{{{3}{x}^{{{2}}}}}{{{2}}}}-{7}{x}+{c}$$
$$\displaystyle={\frac{{{x}^{{{4}}}}}{{{2}}}}-{\frac{{{x}^{{{3}}}}}{{{3}}}}+{\frac{{{3}{x}^{{{2}}}}}{{{2}}}}-{7}{x}+{c}$$

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