Free Printable Integration

1.

a)

⅝

b)

-⅝

c)

⅜

d)

45/16

2.

∫3x²(x³-9)^2/3 dx

a)

(3x²)^4/3

b)

(2/3)(x³-9)^5/3

c)

3(x³-9)^-1/3

d)

-3(x³-9)^-1/3

3.

∫e^xsin(e^x+6) dx

a)

-cos(e^x+6) + C

b)

cos(e^x+6) +C

c)

sin(e^x+6)+C

d)

e^2x/2

4.

$\frac{d}{dx}\left[e^{2x}\ +\ 3x^2+5\right]$

a)

$e^{2x}+\ 6x^2$

b)

$2e^{2x}\ +6x\$

c)

$2e^x+6x\$

d)

none of these

5.

$\int_{ }^{ }e^{5x}dx\ =$

a)

$e^{5x}+c$

b)

$5e^{5x}+c$

c)

$\frac{1}{5}e^{5x}+c$

d)

none of these

6.

∫(cos x + 3x²)dx =

a)

-sin x + x³ + c

b)

sinx + x³ + c

c)

-sin x + 6x

d)

🌞

7.

$\int\ \frac{2}{x+3}dx^{ }=$

a)

2ln|x+3| + c

b)

2ln(x + 3) + c

c)

$\frac{1}{2}\ln\left|x\ +\ 3\right|\ +\ c$

d)

none of these

8.

∫cos(4x+5)dx

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

9.

$\int\left(\frac{4}{x}-e_{ }^x\right)dx$

a)

$4\ln\left(x\right)-e^x$

b)

$4\ln\left(x\right)+e^x+C$

c)

$4\ln\left(x\right)-e^x+C$

d)

$\frac{4}{x^2}-4e^x+C$

10.

Which of the following is TRUE ?

a)

$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +c$

b)

$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ c$

c)

$\int_{ }^{ }\ \frac{1}{x}\ \ dx\ =\ \ln\ \left|x\ \right|\ +c$

d)

$\int_{ }^{ }\ x\ \ dx\ =\ 1\ +\ c$

11.

$\int_{ }^{ }x^3\ -\pi\ dx\ \ =$

a)

$3x^2\ +\ c$

b)

$\frac{x^4}{4}\ +\ c$

c)

$\frac{x^4}{4}\ -\ \pi x$

d)

$\frac{x^4}{4}\ -\ \pi x\ +\ c$

12.

What is $\int_{ }^{ }\ \frac{5}{x^6}\ dx$ ?

a)

$5x^{-6}\ +\ c$

b)

$5x^{-5}\ +\ c$

c)

$-\frac{5}{4x^4}\ +\ c$

d)

$-\frac{1}{x^5}\ +\ c$

13.

Integrate $\int_{ }^{ }\cos\ \left(5x\right)\ dx$ with respect to x.

a)

$\sin\ \left(5x\right)\ +\ c$

b)

$-\frac{1}{5}\sin\ \left(5x\right)\ +\ c$

c)

$\frac{1}{5}\ \sin\ \left(5x\right)\ +\ c$

d)

$\frac{\cos\ \left(5x\right)}{5}\ +\ c$

14.

Which is the integral of $\int_{ }^{ }\ \left(5-3x\right)^3\ dx$ ?

a)

$3\left(5-3x\right)^2\ +c$

b)

$\frac{\left(5-3x\right)^4}{4}+\ c$

c)

$\frac{\left(5-3x\right)^4}{12}+\ c$

d)

$-\frac{\left(5-3x\right)^4}{12}+\ c$

15.

Which of the following is NOT one of techniques of Integration?

a)

Substitution

b)

By Part

c)

Quotient Rule

d)

Partial Fraction

16.

Using integration by part, if given that u = (x + 1) then find v for $\int\left(x\ +1\right)\ e^{2x}\ dx$

a)

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

b)

$e^{2x}$

c)

$2e^{2x}$

d)

$\frac{e^{2x}}{2}$

17.

Integrate the partial fraction with respect to x
$\int_{ }^{ }\ \frac{1}{\left(x\right)}\ +\ \frac{4}{\left(2x\ -1\ \right)}\ dx$

a)

$\ln\ \left|x\right|\ +\ 8\ \ln\left|2x-1\right|+c$

b)

$\ln\ \left|x\right|\ +\ 4\ \ln\ \left|x-1\right|+c$

c)

$\ln\ \left|x\right|\ +\ 4\ \ln\left|2x-1\right|+c$

d)

$\ln\ \left|x\right|\ +\ 2\ \ln\left|2x-1\right|+c$

18.

Evaluate $\int_1^2\ \ 3x^2\ \ dx$

a)

$7$

b)

$8$

c)

$12$

d)

$x^3$

19.

Evaluate the integral $\int_0^2\ \frac{x^3\ +\ x^2}{x^2}\ dx$

a)

$2$

b)

$4$

c)

$6$

d)

$8$

20.

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

a)

$\frac{ax^{n+1}}{n+1}$

b)

$\frac{ax^{n-1}}{n-1}+\ c$

c)

$\frac{ax^{n+1}}{n}+\ c$

d)

$\frac{ax^{n+1}}{n+1}+\ c$

Integration

Total questions: 20

Worksheet time: 40mins

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