Calculus/integrals

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Expert: - 5/2/2009


Question
hi again,
i should know how to do this but im having a mind blank and keep getting the wrong answer

find the integral of f(x)= 2x+4x^(2)-(xsqrt(x))+5e^(x) between 0 and 1

Answer
⌠
⌡ x dx = x²/2 + C1,

⌠
⌡ 4x² dx = 4x^3/3 + C2,

⌠
⌡ x√x =
⌠
⌡ x^(3/2) dx = x^(5/2)/(5/2) + C3 = 2*(x^(5/2))/5 + C3, and

⌠
⌡ 5e^x dx = 5e^x + C4.

Here, C1, C2, C3, and C4 are constants.
They disappear when limits are put into the equations.

For example, x²/2 (0 to 1) is 1²/2 - 0²/2 = 1/2.
5e^x (0 to 1) = 5e^1 - 5e^0 = 5(e-1).

I have demonstrated how to evaluate two of them.
Do the other two in the same fashion.

The fractions you get for doing all four problems will all have to be converted so that they are 30ths.  They then can be added together since they are all over 30.

Calculus

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