How do you integrate #3x^2-5x+9# from 0 to 7?
you have:
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To integrate (3x^2 - 5x + 9) from (0) to (7), you can use the definite integral formula:
[ \int_{0}^{7} (3x^2 - 5x + 9) , dx ]
First, find the antiderivative of the function:
[ \int (3x^2 - 5x + 9) , dx = x^3 - \frac{5}{2}x^2 + 9x + C ]
Then, evaluate this antiderivative at the upper and lower limits of integration:
[ \left[ x^3 - \frac{5}{2}x^2 + 9x \right]_0^7 ]
[ = \left(7^3 - \frac{5}{2} \times 7^2 + 9 \times 7 \right) - \left(0^3 - \frac{5}{2} \times 0^2 + 9 \times 0 \right) ]
[ = \left(343 - \frac{5}{2} \times 49 + 63 \right) - (0 - 0 + 0) ]
[ = \left(343 - \frac{245}{2} + 63 \right) - 0 ]
[ = \left(343 - 122.5 + 63 \right) ]
[ = 283.5 ]
So, the definite integral of (3x^2 - 5x + 9) from (0) to (7) is (283.5).
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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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