Free Printable Integration

1.

∫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

2.

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

a)

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

b)

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

c)

$2e^x+6x\$

d)

none of these

3.

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

a)

$e^{5x}+c$

b)

$5e^{5x}+c$

c)

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

d)

none of these

4.

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

a)

2ln|x+3| + c

b)

2ln(x + 3) + c

c)

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

d)

none of these

5.

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

a)

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

b)

$\frac{3x^2}{2}+7x+c$

c)

$\frac{x^4}{8}+7x+c$

d)

$\frac{x^4}{8}+c$

6.

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

a)

$22\left(2x+1\right)^{11}+c$

b)

$\frac{1}{22}\left(2x+1\right)^{11}+c$

c)

$11\left(2x+1\right)^{10}+c$

d)

$\frac{1}{11}\left(2x+1\right)^{10}+c$

7.

Find the integral with respect to x of $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$

a)

$\frac{e^{6x}}{6}\ +\ c$

b)

$\frac{e^{9x}}{9}\ +\ c$

c)

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

d)

$\left(e^{3x}\right)^2\ +\ c$

8.

What method would you use here?

a)

antiderivatives

b)

u-substitution

c)

integration by parts

d)

slope fields

9.

When using u-substitution to integrate this, what is the u?

a)

2x

b)

e^x

c)

x²

d)

none of these

10.

This can be integrated using u-substitution. What should "u" equal in this integral?

a)

x

b)

(lnx)/x

c)

lnx

d)

sin(lnx)

11.

Solve the following by using substitution method:
$\int\left(\frac{4x}{2x^2+6}\right)dx$

a)

$\ln\left(2x^2+6\right)+c$

b)

$\ln\left(2x^2+6\right)$

c)

$4x\ln\left(2x^2+6\right)+c$

d)

$4x\ln\left(2x^2+6\right)$

12.

∫ x (x² + 7 )^(1/3) dx

a)

(3/4) ( x²+ 7 )^(4/3) + C

b)

(3/8) ( x²+ 7 )^(4/3) + C

c)

( x²+ 7 )^(4/3) + C

d)

(3/2) ( x²+ 7 )^(4/3) + C

13.

What should du equal in this integral?

a)

tanx secx dx

b)

secx dx

c)

sec²x dx

d)

tanx dx

14.

∫(3x⁴+2)⁴(12x³)dx

a)

½(3x⁴+2)⁴+C

b)

(3x⁴+2)⁴+C

c)

⅕(3x⁴+2)⁵+C

d)

⅓(3x⁴+2)⁶+C

15.

Given that $\int_{ }^{ }\frac{12}{\left(2x-3\right)^4}dx=m\left(2x-3\right)^n+c$ , state the value of m and of n.
[Key in the numerical value of m and of n separated by a comma without spacing, e.g. 1,2]

(a)

16.

f''(x) = x³ + x

a)

f(x) = x⁵ / 5 + x² / 2 + c

b)

f(x) = x⁴ / 4 + x² / 2 + c

c)

f(x) = x⁵ / 20 + x³ / 6 + cx + k

d)

f(x) = x⁵ / 20 + x³ / 6 + c

17.

$\int_{ }\frac{2x+1}{x^2+x+1}dx$ by using method of substitution.

a)

$\ln\left|u\right|$

b)

$\ln\left|u\right|+c$

c)

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

d)

$\ln\left|x^2+x+1\right|$

18.

$\int_{ }\frac{\left(\ln3x\right)^4}{x}dx$ by using method of substitution.

a)

$\frac{u^5}{5}$

b)

$\frac{\left(\ln3x\right)^5}{5}+c$

c)

$\ln3x+c$

d)

$\frac{\ln3x}{5}+c$

19.

a)

sec²x +C

b)

ln|cosx| +C

c)

-ln|sinx|+C

d)

-ln|cosx|+C

20.

Find

a)

b)

c)

d)

21.

a)

e^√x+ C

b)

2e^√x+C

c)

¼ e^√x+C

d)

ln√x +C

22.

$\int\ \ \ \frac{\sec^8x}{\operatorname{cosec}\ x}dx$

a)

$\frac{\sec^6x}{6}+c$

b)

$\frac{\sec^7x}{7}+c$

c)

$\frac{\operatorname{cosec}^6x}{6}+c$

d)

$\frac{\operatorname{cosec}^7x}{7}+c$

23.

$\int\sin^{2\ }xdx=$

a)

$\frac{x}{2\ }-\frac{\sin2x}{4}+c$

b)

$\frac{x}{2\ }-\frac{\cos2x}{4}+c$

c)

$\frac{x}{4}-\frac{\sin2x}{4}+c$

d)

$\frac{x}{\ }-\frac{\sin2x}{4}+c$

24.

$\int2\sin3x.\sin6x\ dx$

a)

$\frac{\sin3x}{3\ }-\frac{\sin9x}{9}+c$

b)

$\frac{\cos3x}{3\ }-\frac{\cos9x}{9}+c$

c)

$\frac{\sin2x}{2}-\frac{\sin9x}{9}+c$

d)

$\frac{\sin3x}{3\ }+\frac{\sin9x}{9}+c$

25.

If $f’(x)=8x^3+3x^2–10x–k,\ \ f(0)=-3$ and
f(-1) = 0, find f(x).

a)

$2x^4+x^3–5x^2–7x–3$

b)

$2x^4+x^3+5x^2–7x–3$

c)

$2x^4+2x^3–5x^2–7x–3$

d)

$2x^4+x^3–5x^2–7x+3$

Integration

Total questions: 25

Worksheet time: 49mins

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