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uranmaximum [27]
3 years ago
12

F(x)=3x+1 and g(x)x^2 what would gf(x) be

Mathematics
1 answer:
AlexFokin [52]3 years ago
8 0
<span>3x^3 + 36x^2 + 12x - 21</span>
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Simplify the expression <br> 7y+3x+3-2y+6
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5y + 3x + 9

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Whenever something is multiplied by the same variable, you can combine the coefficients. In this case, first you'd move the values with the same variable next to each other, for simplicity:

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Natalija [7]
Split up the interval [2, 5] into n equally spaced subintervals, then consider the value of f(x) at the right endpoint of each subinterval.

The length of the interval is 5-2=3, so the length of each subinterval would be \dfrac3n. This means the first rectangle's height would be taken to be x^2 when x=2+\dfrac3n, so that the height is \left(2+\dfrac3n\right)^2, and its base would have length \dfrac{3k}n. So the area under x^2 over the first subinterval is \left(2+\dfrac3n\right)^2\dfrac3n.

Continuing in this fashion, the area under x^2 over the kth subinterval is approximated by \left(2+\dfrac{3k}n\right)^2\dfrac{3k}n, and so the Riemann approximation to the definite integral is

\displaystyle\sum_{k=1}^n\left(2+\frac{3k}n\right)^2\frac{3k}n

and its value is given exactly by taking n\to\infty. So the answer is D (and the value of the integral is exactly 39).
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