Free Printable Introduction to Integrals

1.

Evaluate: $\int2x\ dx$

a)

$2x+C$

b)

$2+C$

c)

$x^2+C$

d)

$\frac{2x^3}{3}+C$

2.

Evaluate $\int5x^3+2x\ \ dx$

a)

$15x^2+2+C$

b)

$5x^4+2x^2+C$

c)

$\frac{1}{5}x^4+\frac{1}{2}x^2+C$

d)

$\frac{5}{4}x^4+x^2+C$

3.

Evaluate $\int\sin x\ dx$

a)

$\cos x\ +C$

b)

$-\cos x+C$

c)

$-\sin x+C$

d)

$\frac{1}{2}\sin x^2+C$

4.

Let $f\left(x\right)=\frac{6}{x^2}$ be a differential equation. Find the general solution.

a)

$F\left(x\right)=\frac{18}{x^3}+C$

b)

$F\left(x\right)=-\frac{12}{x}+C$

c)

$F\left(x\right)=-\frac{6}{x}+C$

d)

$F\left(x\right)=-\frac{2}{x^3}+C$

5.

Which of the following will give a displacement function as a general solution? Note: a(t) is an acceleration function, v(t) is a velocity function, and s(t) is a displacement function.

a)

$\int v\left(t\right)dt$

b)

$\int a\left(t\right)dt$

c)

$\int s\left(t\right)\ dt$

d)

$\int a'\left(t\right)dt$

6.

Evaluate $\int\sqrt{x}dx$

a)

$x^{\frac{1}{2}}+C$

b)

$\frac{1}{2}x^{-\frac{1}{2}}+C$

c)

$x^{\frac{3}{2}}+C$

d)

$\frac{2}{3}x^{\frac{3}{2}}+C$

7.

Evaluate $\int7x-9x_{ }^{-3}-2\ \ dx$

a)

$F\left(x\right)=7+27x^{-4}+C$

b)

$F\left(x\right)=\frac{7}{2}x^2+\frac{9}{2}x^{-2}-2x+C$

c)

$F\left(x\right)=7x^2-9x^{-2}-2x+C$

d)

$F\left(x\right)=7x^0-9x^{-4}-2x^{-1}+C$

8.

Evaluate $\int e^xdx$

a)

$2e^{2x}+C$

b)

$e^{2x^2}+C$

c)

$e^{\frac{1}{2}x^2}+C$

d)

$e^x+C$

9.

Evaluate $\int\ \frac{1}{x}\ dx$

a)

$\ln x+C$

b)

$e^x+C$

c)

$1+C$

d)

$e^{-x}+C$

10.

List any questions you have at this time. What are you wondering?

4 lines

Introduction to Integrals

Total questions: 10

Worksheet time: 50mins

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