Topic

# Definite Integrals

Topic Progress:

\begin{aligned} \displaystyle \int_{a}^{b}{x^n}dx &= \Big[\dfrac{x^{n+1}}{n+1}\Big]_{a}^{b} \\ &= \dfrac{b^{n+1}}{n+1} - \dfrac{a^{n+1}}{n+1} \end{aligned}

## Practice Questions

### Question 1

Evaluate $\displaystyle \int_{1}^{2}{2x}dx$.

### Question 2

Evaluate $\displaystyle \int_{0}^{2}{6x}dx$.

### Question 3

Evaluate $\displaystyle \int_{2}^{4}5dx$.

### Question 4

Evaluate $\displaystyle \int_{1}^{3}{(2x+4)}dx$.

### Question 5

Evaluate $\displaystyle \int_{0}^{1}{4}dx$.

### Question 6

Evaluate $\displaystyle \int_{1}^{3}{(6x^2 - 10x)}dx$.

### Question 7

Evaluate $\displaystyle \int_{-1}^{2}{(x+2)(x-1)}dx$.

### Question 8

Evaluate $\displaystyle \int_{-1}^{1}{6\sqrt[3]{x}}dx$.

### Question 9

Evaluate $\displaystyle \int_{0}^{1}{\dfrac{1}{\sqrt{3+2x}}}dx$.

### Question 10

Evaluate $\displaystyle \int_{0}^{2}{(2x-1)^3}dx$.

### Question 11

Evaluate $\displaystyle \int_{0}^{1}{(2x-1)^3}dx$.

### Question 12

Evaluate $\displaystyle \int_{-1}^{4}{\sqrt{3x+4}}dx$.

### Question 13

Evaluate $\displaystyle \int_{1}^{3}{\dfrac{x-2}{x^3}}dx$.

### Question 14

Evaluate $\displaystyle \int_{2}^{3}{\dfrac{3}{(2x+3)^2}}dx$.

### Question 15

Find $k$, if $\displaystyle \int_{2}^{3}{(2x+k)}dx = 9$.

### Question 16

Find $\displaystyle \dfrac{d}{dx}\int_{3}^{x}{(4t^3-3t^2+2t-1)}dx$.