APPLICATIONS OF INTEGRATION WORKSHEET

About "Applications of Integration Worksheet"

Applications of Integration Worksheet :

Here we are going to see some practice problems based on applications of integration.

Applications of Integration Worksheet - Practice Questions

(1)  If f'(x)  =  4x - 5 and f(2)  =  1, find f(x)

Solution

(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)

Solution

(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)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?

Practice Questions on Definite Integrals

(1)  Integrate the following with respect to x

∫ [(x + 4)+ 5/(2 - 5x)4 - cosec2(3x - 1)] dx

Solution

(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"

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OTHER TOPICS

Profit and loss shortcuts

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Domain and range of rational functions

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Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

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Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 