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# Worksheets of Application of Integration

Test your skills on Application of Integration by trying out Application of Integration worksheets. 9 Application of Integration worksheets available to gain expertise and excel in your grades. The worksheets on Application of Integration have been designed to offer a wide range of questions covering all details of the Application of Integration and are in compliance with the k-12 curriculum. Detailed answers will be provided after you have attempted the Application of Integration worksheet. Each worksheet will have around 10 questions and there are multiple worksheets available to try out.

• ## Area Between Curves Worksheet

1. Calculate the area of region between two curves y = x2 and y = ?
• 1/4
• 3/2
• 1/3
• 1/13
2. Calculate the area of region bounded by x = 2, y = x + 1 and y =  and y- axis?
• 4.521
• 3.5092
• 3.0000
• 2.9090
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• ## Area of Region Bounded by Parametrically Defined or Polar Curves Worksheet

1. Find the area of region bounded parametrically, when first polar curve f (Ńł) = sin Ńł and other polar curve is g(Ńł) = cos Ńł, and these curve s lie between [-π/2, π/2]?
• 2
• 0
• 3
• 1
2. Find the area of region bounded by parametrically where one polar curve is f (Ńł) = 2cos Ńł and other polar curve is g (Ńł) = sin2Ńł, and these curve s are lie between [-π/2, π/2] interval?
• (π + 8)/2
• (π - 8)/2
• (π - 8)
• 0
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• ## Velocity and Distance Problems Involving Motion Along a Line Worksheet

1. A car starts moving straight with 50 miles/hr speed from Sydney and reach Melbourne in 120 minutes, then find out the distance traveled by car?
• 100 miles
• 120 miles
• 125 miles
• 123 miles
2. A train starts from station ‘A’ at 9.00 am and reaches station ‘B’ at 01.00 pm. If the speed of the train is 50miles/hr, then find the distance between ‘A’ and ‘B’?
• 250 miles
• 225 miles
• 200 miles
• 210 miles
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• ## Other Applications Involving the Use of Integral of Rates Worksheet

1. A bullet is fired vertically upwards from surface at 25 m / s. Find the height of bullet after 3.5 s?
• 23.654 m
• 32.765 m
• 25.555 m
• 27.475 m
2. If electric current represented as a function of time given by i = 0.5 – 0.4 t, in a calculator circuit. Find the total charge passing from a point in circuit in 0.60 s?
• 0.45
• 1.43
• 0.54
• 0.05
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• ## Area of Region Worksheet

1. Find the area enclosed with the region of the following equations: u = k3 + k2 -6k and the k-axis?
• 352 / 5
• 253 / 2
• 765 / 3
• 253 / 12
2. Find the bounded area enclosed with the given equations u = k2 and u = 8 – k2?
• 76 / 5
• 64 / 3
• 78 / 5
• 64 / 5
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• ## Volumes of Solid of Revolutions Worksheet

1. Find out the volume created by rotating the region bounded by the curves k = u2, the u- axis and the line u = 2 about u axis?
• 32 π / 5
• 39 π / 7
• 22 π /  5
• 20 π /  7
2. If the region formed by the curves k = u2, the k - axis and the line k = 9 is rotated about the k axis then find out the volume of the solid that is generated by the rotation of these curves?
• (71 π) / 3
• (71 π) / 2
• (81 π) / 3
• (81 π) / 2
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• ## Arc Length Worksheet

1. Determine the arc length of y = log (sec x) where ‘x’ lies between o to π/4?
• log (√2)
• log (√2 + 1)
• log (√3 + 1)
• log (√5 + 1)
2. Calculate the arc length of the function f(x) = x3/2 over the interval [0, 1]?
• 1.44
• 2.45
• 3.46
• 4.44
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• ## Applications of Integration Worksheet

1. Calculate the average value of the following function on the interval given, f ( x ) = x2 - 5x + 6 cos ( πx ) on the interval [-1, 5/2 ]?
• -1.620
• 7.250
• 2.620
2. Calculate the number ‘k’ that satisfies the mean value theorem for integrals for the function on the interval [ 1, 4 ], where f(t) = t2 + 3t + 2?
• 2.593
• -5.593
• 3.593
• 4.593
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• ## Velocity and acceleration vectors of Planar curves worksheet

1. Find the velocity vector of a particle whose equation of the motion is given as, x ( t ) = t 2 + 5 t 3 and y ( t ) = t 3 – t 5
here, ‘t’ is representing the time variable. Calculate the velocity vector at t = 3?
• (141 , - 378 )
• ( 200 , 475 )
• ( - 378 , 141 )
• ( 339, 219 )
2. Evaluate the acceleration vector for the particle whose equation of motion is given as, x ( t ) = t + 7 t 4, y ( t ) = 2 t + 3 t 2, At time t = 2?
• (997, - 5)
• (112 , 6)
• (244 , 5)
• (336, 6)
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