Free Printable FIRST QUIZ IN INTEGRAL CALCULUS

1.

$_{Evaluate\ the\ \int_{ }^{ }x\cos4x\ dx}$

a)

$\frac{x\cos4x}{4}+\frac{\cos4x}{16}\ +\ c$

b)

$\frac{x\sin4x}{4}\ +\ \frac{\cos4x}{16}\ +\ c$

c)

$\frac{x\sin4x}{4}\ -\ \frac{\cos4x}{16}\ +\ c$

d)

$\frac{xsun4x}{4}\ +\ \frac{\cos4x}{16}\ +\ c$

2.

$Evaluate\ the\ \int_{ }2x^2e^{4x}\ dx$

a)

$\frac{x^2e^{4x}}{2}\ -\ \frac{xe^{4x}}{4}+\frac{e^{4x}}{16}\ +\ c$

b)

$\frac{x^2e^{4x}}{2}\ -\ \frac{xe^{4x}}{4}-\frac{e^{4x}}{16}\ +\ c$

c)

$\frac{x^2e^{4x}}{2}\ +\ \frac{xe^{4x}}{4}+\frac{e^{4x}}{16}\ +\ c$

d)

$-\frac{x^2e^{4x}}{2}\ -\ \frac{xe^{4x}}{4}+\frac{e^{4x}}{16}\ +\ c$

3.

$The\ antiderivative\ of\ 4xe^{2x}\ dx\ is\ 2xe^x-e^{2x}\ +\ c$

a)

True

b)

False

4.

$Evaluate\ the\ \int_{ }^{ }e^{2x}\sin6x\ dx$

a)

$\frac{e^{2x}\sin6x}{10}\ -\ \frac{3e^{2x}\cos6x}{20}\ +\ c$

b)

$\frac{e^{2x}\sin6x}{20}\ -\ \frac{3e^{3x}\cos6x}{20}\ +\ c$

c)

$-\frac{e^{2x}\sin6x}{20}\ -\ \frac{3e^{2x}\cos6x}{20}\ +\ c$

d)

$\frac{e^{2x}\sin6x}{20}\ -\ \frac{3e^{2x}\cos6x}{20}\ +\ c$

5.

Integration by algebraic substitution is used when a certain algebraic function can't be integrated directly.

a)

True

b)

False

6.

*Write your answer in ALL CAPITAL LETTERS.

Integral calculus involves integrating all kinds of functions like polynomial functions, trigonometric functions, exponential functions, logarithmic functions, inverse trigonometric functions, (a) functions and complex functions.

7.

$Evaluate\ the\ \int_{ }^{ }3x^2\operatorname{arccot}x\ dx$

a)

$x^3\operatorname{arccot}x\ -\ \frac{x^2}{2}-\frac{\ln\left|1\ +\ x^2\right|}{2}+\ c$

b)

$x^3\operatorname{arccot}x\ +\ \frac{x^2}{2}-\frac{\ln\left|1\ +\ x^2\right|}{2}+\ c$

c)

$x^3\operatorname{arccot}x\ +\ \frac{x^2}{2}-\frac{\ln\left|1\ -\ x^2\right|}{2}+\ c$

d)

$x^3\operatorname{arccot}x\ -\ \frac{x^2}{2}+\frac{\ln\left|1\ -\ x^2\right|}{2}+\ c$

FIRST QUIZ IN INTEGRAL CALCULUS

Total questions: 7

Worksheet time: 40mins

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