Find the area under the given curve over the indicated interval.
$y = x^{2} + x + 2; [4, 6]$

Answer

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Answer

Final Answer: The area under the curve over the indicated interval is $\frac{194}{3}$ .

Steps

Step 1 ：We are given the function $y = x^{2} + x + 2$ and we need to find the area under the curve from $x = 4$ to $x = 6$ .

Step 2 ：The area under a curve from a to b is given by the definite integral of the function from a to b.

Step 3 ：So, we need to find the definite integral of the function $y = x^{2} + x + 2$ from 4 to 6.

Step 4 ：By calculating the definite integral, we find that the area under the curve over the indicated interval is $\frac{194}{3}$ .

Step 5 ：Final Answer: The area under the curve over the indicated interval is $\frac{194}{3}$ .