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# Worksheets of Integration

Test your skills on Integration by trying out Integration worksheets. 5 Integration worksheets available to gain expertise and excel in your grades. The worksheets on Integration have been designed to offer a wide range of questions covering all details of the Integration and are in compliance with the k-12 curriculum. Detailed answers will be provided after you have attempted the Integration worksheet. Each worksheet will have around 10 questions and there are multiple worksheets available to try out.

• ## Trigonometric Worksheet

1. Differentiate the function f (x) where f (x) = 3 sin (x) - 4 sin (x)?
• 3 sin (x) + 4 cos (x)
• 3 cos (x) + 4 sin (x)
• 2 sin (x) + 4 cos (x)
• 5 sin (x) + 8 cos (x)
2. Differentiate the function f ( x ) = x 3 tan ( x )?
• 2( x sec 2 x + 3 tan x )
• x2 ( cosec 2 x + 3 tan x )
• x2 ( sec x + 3 tan x )
• x2 ( sec x + 3 tan2 x )
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• ## Fourier Series and Laplace Transform Worksheet

1. Find out the Laplace transform of the function given below:
f(t) = t when 0 ≤ t ≤ ( ½ )
f(t) = t – 1 when ( ½ )≤ t ≤ 1
f(t) = 0 when t > 1?
• (1/s2) [ (e-s - 1) + se(-s/2)]
• (1/s2) [ (e-s - 1) + se(-s/2)]
• (1/s2) [ (e-s - 1) + se(-s/2)]
• (1/s2) [ (e-s - 1) + se(-s/2)]
2. Find out the Laplace transform of the function f(t) = (1/t2) (1 – cos t)?
• s log s / √(s2 + 1) + tan-1 (3/s)
• s log s / √(2s2 + 1) + tan-1 (2/s)
• s log 2s / √(s2 + 1) + tan-1 (2/s)
• s log s / √(s2 + 1) + tan-1 (1/s)
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• ## Power Rule Worksheet

1. Determine derivative of the function y = (-x2) using power rule?
• -2 x
• -3 x
• - x
• -4 x
2. Find d/dx (-1/x2) using power rule?
• -1/x2
• -3 x
• 2/x3
• -4 x
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• ## Fourier Cosine Transform Worksheet

1. Find the cosine transformation for Fourier series where  function f(t) = cos (πpt)?
• f(u)   = ½ δ(u-p) + δ(u +)p
• f(u)   = ½ δ(u-p) + ½ δ(u -p)
• f(u)   = ½ δ(u-q) +  δ(u q)
• f(u)   = ½ δ(u-p) + ½ δ(u +p)
2. Find the cosine transformation for Fourier series where function f(x) = eax where interval of this function is (-π, π)?
• n = (a(-1)n sinh(aπ))/π(a2+n2)
• n = (2a(1)n sinh(aπ))/π(a2+n2)
• n = (2a(-1)n sinh(aπ))/π(a2+n2)
• n = (2(-1)n sinh(aπ))/π(a2+n2)
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• ## Areas of Bounded Region Worksheet

1. Find out the area bounded by two regions k = u2 and k = √u?
• 2/3
• 3/2
• 1/3
• 3
2. Find out the area of the region enclosed by k = u e(u2), k = u+1, u = 2 and the k-axis?
• 2.489
• 7.987
• 4.905
• 3.509
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