Home > Calculus > Formal Definition of the Definite Integral

How do you find the definite integral for: # x^2 + x + 4# for the intervals [0,2]?

Answer 1

Aurora Alvarado

#38/3#

To integrate this function use the #color(blue)"power rule"#

#int(ax^n)dx=(ax^(n+1))/(n+1)# which can be applied to each term.

#rArrint_0^2(x^2+x+4)dx=[x^3/3+x^2/2+4x]_0^2#

now subtract the value of the lower limit from the value of the upper limit.

#rArr(8/3+2+8)-(0)=38/3#

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Answer 2

Ezekiel Alexander

To find the definite integral of (x^2 + x + 4) over the interval ([0, 2]), you integrate the function with respect to (x) and then evaluate the result at the upper and lower limits of the interval.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.