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basic Integration

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I have three questions which I apparently have 'wrong' according to the book, but I've done lots of other questions which I've gotten right using the same method and I have triple checked these answers for these three questions so I was wondering if someone could tell me if I actually do have these answers wrong or if its the book?

Find the areas enclosed by the x-axis and these curves and straight lines

a) y= (1/8)x^3 + 2x, x=2, x=4
for this I got 132 sq units, but the book says 19.5

b) y=6-(1/(sqrt x)), x=16, x=25
for this I got 53 sq units and in the book it says 52

c) y= (3x-4)^2, x=1, x=3
for this I got 13 sq units but the book says its 14 sq units

Thanks in advance!

  • basic Integration - ,

    a) The integral of the function from 2 to 4 is the difference in values of
    x^4/32 + x^2 at the two points. That would be 8 + 16 - 0.5 - 4 = 19.5

    b) The indefinite integral is
    6x - 2 x^1/2
    The difference in that function at the two limits is
    150 - 10 - 96 + 8 = 52

    I suggest you check your math again, or the way you are doing the integration.

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