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Please help and explain :)))

Please help and explain :)))-example-1

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Answer:

negative

Explanation:

You want to know if the integral of f(x) = 1/5(x³ -7x² +10x) on the interval 0 to 5 is positive or negative, given a graph of the function.

Area

The integral of a function gives you the area between the function's graph and the x-axis. Area above the axis is positive, and area below the axis is negative.

In the attachment, the positive area is shaded green, and the negative area is shaded red. The purpose of this shading is to show you which area has what sign, and to help you see that the red area is larger than the green area.

Since there is more negative area than positive area, the value of the definite integral will be negative. (The graphing calculator shows you the value is about -25/12.)

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Additional comment

The above description of the value of the integral is true if the lower integration limit is lower than the upper integration limit. If the integral is in the other direction, the signs of the areas are reversed.

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Please help and explain :)))-example-1
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