Applications of Integration Worksheet :
Here we are going to see some practice problems based on applications of integration.
(1) If f'(x) = 4x - 5 and f(2) = 1, find f(x)
(2) If f'(x) = 9x2 - 6x and f(0) = -3, find f(x)
(3) If f''(x) = 12x - 6 and f(1) = 30, f'(1) = 5 find f(x)
(4) A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find
(i) how long will it take for the ball to strike the ground?
(ii) the speed with which will it strike the ground? and
(iii) how high the ball will rise? Solution
(5) A wound is healing in such a way that t days since Sunday the area of the wound has been decreasing at a rate of -3/(t+2)2 cm2 per day. If on Monday the area of the wound was 2cm2
(i) What was the area of the wound on Sunday?
(ii) What is the anticipated area of the wound on Thursday if it continues to heal at the same rate?
(1) Integrate the following with respect to x
∫ [(x + 4)5 + 5/(2 - 5x)4 - cosec2(3x - 1)] dx
(2) Integrate the following with respect to x
∫ [4 cos (5-2x) + 9e3x-6 + 24/(6-4x)] dx
(3) Integrate the following with respect to x
∫ [sec2(x/5) + 18 cos 2x + 10 sec (5x + 3) tan (5x + 3)] dx
(4) Integrate the following with respect to x
∫ [8/√(1 - (4x)2) + 27/√(1 - 9x2) - 15/(1+25x2)] dx
(5) Integrate the following with respect to x
∫ [6/(1 + (3x + 2)2)] - [12/√1 - (3-4x)2] dx
(6) Integrate the following with respect to x
∫ (1/3) cos ((x/3) - 4)) + 7/(7x+9) + e(x/5) + 3 dx
After having gone through the stuff given above, we hope that the students would have understood, "Applications of Integration Worksheet"
Apart from the stuff given in "Applications of Integration Worksheet", if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions