How do you evaluate the definite integral #int (6x^2)dx# from [0,7]?

Answer 1

686

#int_0^7 6x^2 dx =[6*x^3/3]_0^7#
#= 2*7^3 - 0 = 2xx343#
#=686#
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Answer 2

To evaluate the definite integral ∫(6x^2)dx from 0 to 7, you need to use the fundamental theorem of calculus. First, find the antiderivative of 6x^2, which is 2x^3. Then, evaluate 2x^3 at the upper limit (7) and subtract the value at the lower limit (0).

So, ∫(6x^2)dx from 0 to 7 = [2(7)^3] - [2(0)^3] = 2(343) - 0 = 686.

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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.

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.

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.

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.

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