Free Printable Fourier series Basics

1.

The value of sin $n\pi$ is

a)

1

b)

0

c)

-1

d)

n

2.

The value of cos $n\pi=$ ------ and Cos 0=-------

a)

0 and 0

b)

$\left(-1\right)^n$ and 0

c)

$\left(-1\right)^n$ and 1

d)

1 and 1

3.

The value of cos $2\pi$ and cos $\pi$

a)

0 and 0

b)

1 and 1

c)

1 and -1

d)

-1 and -1

4.

The value of $\int_{ }^{ }\cos5x\ dx$ =

a)

5 sin5x

b)

-5sin5x

c)

$\frac{\sin5x}{5}$

d)

$-\frac{\sin5x}{5}$

5.

The value of $\int_0^{\pi}\ \sin3x\ dx$

a)

$\frac{2}{3}$

b)

$-\frac{2}{3}$

c)

0

d)

$\frac{1}{3}$

6.

$\frac{\text{d}}{\text{d}x}\left(x^2\right)\ =$

a)

x

b)

2

c)

2x

d)

0

7.

$\frac{\text{d}}{\text{d}x}\left(k\right)=$ -------where k is constant

a)

1

b)

k

c)

0

d)

x

8.

$\int_0^{2\pi}\ \ x\ \sin x\ dx$ =

a)

$\left|x\left(-\cos x\right)-\left(-\sin x\right)\right|$

b)

$\left|x\left(\cos x\right)-\left(\sin x\right)\right|$

c)

$\left|x\left(-\cos x\right)-\left(-\sin x\right)\right|_0^{2\pi}\ =\ 0$

d)

$\left|x\left(-\cos x\right)-\left(-\sin x\right)\right|_0^{2\pi}\ =\ -2\pi$

9.

$\int_0^{2\pi}\ x\ \cos nx\ dx\ =$

a)

$\left|x\left(\sin x\right)\left(-\cos x\right)\right|$

b)

$\left|x\left(\frac{\sin nx}{n}\right)-\left(-\frac{\cos nx}{n^2}\right)\right|$

c)

$\left|x\left(\frac{\sin nx}{n}\right)-\left(-\frac{\cos nx}{n^2}\right)\right|_0^{2\pi}\ \ =0$

d)

$\left|x\left(\frac{\sin nx}{n}\right)-\left(-\frac{\cos nx}{n^2}\right)\right|_0^{2\pi}\ =2$

10.

$\int_0^{2\pi}\ x\ \cos\left(\frac{n\pi}{l}\ \right)x\ dx\ =$

a)

$\left|x\left(\sin\left(\frac{n\pi}{l}\ \right)x\right)\left(-\cos\left(\frac{n\pi}{l}\ \right)x\right)\right|$

b)

$\left|x\left(\frac{\sin\left(\frac{n\pi}{l}\ \right)x}{\left(\frac{n\pi}{l}\ \right)}\right)-\left(-\frac{\cos\left(\frac{n\pi}{l}\ \right)x}{\left(\frac{n\pi}{l}\ \right)^2}\right)\right|$

c)

$\left|x\left(\frac{\sin\left(\frac{n\pi}{l}\ \right)x}{\left(\frac{n\pi}{l}\ \right)}\right)-\left(-\frac{\cos\left(\frac{n\pi}{l}\ \right)x}{\left(\frac{n\pi}{l}\ \right)^2}\right)\right|_0^{2\pi}\ \$

= 0

d)

$\left|x\left(\frac{\sin nx}{n}\right)-\left(-\frac{\cos nx}{n^2}\right)\right|_0^{2\pi}\$
=2

Fourier series Basics

Total questions: 10

Worksheet time: 7mins

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