Fundamental theorem of calculus

  • Thread starter staples82
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  • #1
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Homework Statement


Evaluate each definite integral.

ok I'm not sure how to do the integration sign, but... b=4, a=1 for (5yy^.5)+3y^.5)dy

Homework Equations





The Attempt at a Solution


I'm not really sure what i'm doing wrong.

i integrated...[tex]5y^2/2*y^(3/2)/(3/2)+3y^(3/2)/(3/2)

then i plugged in stuff so...F(b)-F(a)...f(4)-(f1)

I got (40*8/3+16)-(5/2*2/3+2) which gave me 357/3...the correct answer is 76 and I have no idea what I'm doing wrong, I've redone this problem 5 times and doublechecked to no avail :-(
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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[tex]\int_1 ^{4}(5yy^\frac{1}{2} + 3y^\frac{1}{2})dy \equiv \int_1 ^{4}(5y^\frac{3}{2} + 3y^\frac{1}{2})dy[/tex]



Remember that y^m * y^n=y^(m+n)
 
  • #3
Dick
Science Advisor
Homework Helper
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[tex]\int_1 ^{4}(5yy^\frac{1}{2} + 3y^\frac{1}{2})dy \equiv \int_1 ^{4}(5y^\frac{3}{2} + 3y^\frac{1}{2})dy[/tex]



Remember that y^m * y^n=y^(m+n)
And remember that you need to use that rule, because you can't integrate a product by taking the product of the integrals.
 

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