midtermReviewToPost.mw

HERE THERE IS A LIST OF THE ANSWERS SO YOU CAN COMPARE THEM WITH 

YOUR RESULTS. IT IS NOT A DETAILED SOLUTION. 

IN THE EXAM, YOU NEED TO SHOW ALL THE STEPS OF YOUR WORK. 

 

 

 

int(Typesetting:-msubsup(Typesetting:-mo( 

int(sin(sqrt(x)), x) = 2*sin(sqrt(x))-2*sqrt(x)*cos(sqrt(x))+C 

 

 

EX 3 

int((2*x^2+5)/((x^2+1)*(x^2+4)), x) = arctan(x)+1/2*arctan(1/2*x)+C 

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EX 4 

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int(1/(1+x^2+x^4), x = 0 .. 6) 

Approximate by midpoint rule, n=6 

 

Δx=(6-0)/6=1 

 

f(x)=1/(1+x^2+x^4) 

x0=0, x1=1, x2=2, x3=3, x4=4, x5=5, x6=6 

 

x1*=1/2, x2*=3/2, x3*=5/2, x4*=7/5, x5*=9/2, x6*=11/2 

 

Apprixmation by midpoint rule is 

 

 

1. Δx(f(x1*)+f(x2*)+f(x3*)+f(x4*)+f(x5*)+f(x6*))= 

+++ 

 

++  

Plot 

 

 

 

 

Apprixmation by trapezoidal rule is 

 

 

1. (Δx/2 )(f(x0)+2f(x1)+2f(x2)+2f(x3)+2f(x4)+2f(x5)+f(x6))= 

+++ 

 

++  

 

 

Plot 

 

 

EX 5  20/3   

 

 

int(abs(x)-x^2+2, x = -2 .. 2)=2int(abs(x)-x^2+2, x = 0 .. 2) = 2*int([0]^2*x-x^2+2, x) and 2*int([0]^2*x-x^2+2, x) = 20/3 

 

EX 6 

 

 

 

Plot 

EX 7