Use the Fundamental Theorem of Calculus to find the "area under curve" of y = − x 2 + 7 x between x = 1 and x = 5 . In your calculations, if you need to round, do not do so until the very end of the problem.

The area under the curve is 42.67 square unit.

Area under curve measures the entire two-dimensional area underneath the entire region of curve.

Area under the curve of f(x), from x = a to x = b is given by,

Here given that,     and  

Substituting above values in Area integral expression.

Substituting the limit of integration.

Thus, the area under the curve is 42.67 square unit.

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The area under the curve is of 42.67 area units.

Step-by-step explanation:

Using the Fundamental Theorem of Calculus, the area under a curve f(x), between and , is given by:

In this question, we have that:

, from 1 to 5. So

The area under the curve is of 42.67 area units.

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step-by-step explanation: