An elementary antiderivative

Calculus Level 1

Evaluate

∫ 1 3 3 x 2 + 2 x d x \int_1^3 3x^2 + 2x \ dx


The answer is 34.

Denton Young by Denton Young , 47, USA

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2 solutions

Denton Young
Sep 5, 2019

The antiderivative of the given function is x 3 + x 2 x^3 + x^2 .

3 3 + 3 2 = 36 3^3 + 3^2 = 36 , and 1 3 + 1 2 = 2 1^3 + 1^2 = 2 .

36 - 2 = 34.

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@Denton Young , an easier way to enter the LaTex code as appeared above \ [ \backslash [ \int_1^3 3x^2 + 2x \ dx \ ] \backslash] . { } is unnecessary if it is only one character. Backslash followed by a space is space.

Chew-Seong Cheong - 1 year, 9 months ago

I = ∫ 1 3 3 x 2 + 2 x d x = x 3 + x 2 ∣ 1 3 = 27 + 9 − 1 − 1 = 34 \begin{aligned} I & = \int_1^3 3x^2 + 2x \ dx \\ & = x^3 + x^2 \ \big|_1^3 \\ & = 27+9 - 1 - 1 \\ & = \boxed{34} \end{aligned}

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