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# Applications of Integration Worksheet

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. -1.620
2. 7.250
3. 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?
1. 2.593
2. -5.593
3. 3.593
4. 4.593
• 3. Calculate the volume of the solid obtained by rotating the region bounded by, y = x2 – 4x + 5, x = 1, x = 4 and the x-axis?
1. 4 π / 9
2. 78 π / 5
3. 87 π / 7
4. 47 π / 9
• 4. Calculate the volume of the solid obtained by rotating the portion of the region bounded by the following functions y = 3√x and y = x / 4 and that lies in the first quadrant about the y- axis?
1. 736 π / 14
2. 512 π / 21
3. 512 π / 14
4. 736 π / 21
• 5. Calculate the volume of the solid obtained by the rotation of the region bounded by the curves x = ( y – 2 )2 and y = x about the line y = -1?
1. 63π / 3
2. 67π/ 2
3. 63π / 2
4. 67π / 3
• 6. A spring has a length of 20m, a force of 40 N is required to stretch that spring or hold that to a length 0f 30m. Calculate the work that is needed in stretching the spring from 35m to 38m?
1. 483 J
2. 438 J
3. 348 J
4. 843 J
• 7. A cable that weighs 2 lbs / ft is attached to a bucket that is filled with coal that weighs 800 lbs. Consider the bucket is initially at the bottom of a 500 ft mine shaft. Then calculate the amount of the work required to lift the bucket to the midpoint of the shaft?
1. 387500
2. 467900
3. 34579
4. 234500
• 8. In the above problem if we need to move the cable from x = 250 to x = 500. Then calculate the work required to move the cable?
1. 343500
2. 197868
3. 262500
4. 787900
• 9. Determine the average value of the function given below on the interval [ -π, π ] and F( x ) = sin ( 2x )e1-cos2π?
1. 34
2. 20
3. 0
4. 98
• 10. Calculate the area bounded by the curves k = 2u2 + 10, k = 4u + 16, u = -2, u = 5?
1. 48.99
2. 54.33
3. 189/3
4. 142/3
Math Topics