Home > Calculus > Formal Definition of the Definite Integral

How do you find the definite integral for: #(6x+3)dx# for the intervals #[3, 9]#?

Answer 1

Ezra Adams

234

#int_3^9(6x+3)dx=[3x^2+3x]_3^9# #=[3(9)^2+3(9)]-[3(3)^2+3(3)]# #=270-36=234#

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Answer 2

Evelyn Agard

To find the definite integral of (6x+3)dx over the interval [3, 9], you first need to find the antiderivative of the function, which is (3x^2 + 3x). Then, you evaluate this antiderivative at the upper and lower limits of integration (9 and 3, respectively) and subtract the result of the lower limit from the result of the upper limit. In this case, it would be [(39^2 + 39) - (33^2 + 33)]. After calculating this expression, you will get the definite integral value.

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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.