Transcription of Integral Calculus - Exercises
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Integral Calculus - Exercises
Integral Calculus - Indefinite IntegralIn problems 1 through 7,find the indicated xdx=Zx12dx=23x32+C=23x x+ + (3x2 5x+2) (3x2 5x+2)dx=3Zx2dx 5Z xdx+2 Zdx==3 13x3 5 23x x+2x+C==x3 23x 5x+2x+ 12x 2x2+3 x 12x 2x2+3 x dx=12Z1xdx 2Zx 2dx+3Zx 12dx==12ln|x| 2 ( 1)x 1+3 2x12+C==ln|x|2+2x+6 x+ Calculus - 2ex+6x+ln2 2ex+6x+ln2 dx=2 Zexdx+6Z1xdx+ln2 Zdx==2ex+6ln|x|+(ln2)x+ +3x 2 +3x 2 xdx=Zx32dx+3Zx12dx 2Zx 12dx==25x52+3 23x32 2 2x12+C==25x52+2x32 4x12+C==25x2 x+2x x 4 x+ (x3 2x2) 1x 5 (x3 2x2) 1x 5 dx=Z(x2 5x3 2x+10x2)dx==Z( 5x3+11x2 2x)dx== 5 14x4+11 13x3 2 12x2+C== 54x4+113x3 x2+ Find the functionfwhose tangent has slopex3 2x2+2for each valueofxand whose graph passes through the point(1,3). slope of the tangent is the derivative (x)=x3 2x2+2and sof(x)is the indefinite integralf(x)=Zf0(x)dx=Z x3 2x2+2 dx==14x4+2x+2x+ Calculus - EXERCISES42 Using the fact that the graph offpasses through the point(1,3)youget3=14+2+2+CorC= , the desired function isf(x)=14x4+2x+2x It is estimated thattyears from now the population of a certain lakesidecommunity will be changing at the rate + + per year.
INTEGRAL CALCULUS - EXERCISES 42 Using the fact that the graph of f passes through the point (1,3) you get 3= 1 4 +2+2+C or C = − 5 4. Therefore, the desired function is f(x)=1 4
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