Definite Integrals Exercises

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• Integrand: (8 – 2y)

• Lower limit of integration: -10

• Upper limit of integration: 0

• Variable of integration: y

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• Integrand: g(t)

• Lower limit of integration: 4

• Upper limit of integration: 10

• Variable of integration: t

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• Integrand: x²

• Lower limit of integration: 0

• Upper limit of integration: 7

• Variable of integration: x

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• The integral of the function g(t) on the interval [8, 9] is

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• Saying "from x = -2 to x = 5" means the same thing as saying "on the interval [-2, 5]." The integral of 6x² from x = -2 to x = 5 is

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• The integral of y from y = a to y = b is

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Since f is a constant function, the region between f and the x-axis on [-10, 2] is a rectangle with length 12 and height 5:

The area of this rectangle is 12 ⋅ 5 = 60, so 

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• This downward sloping line forms a triangle and a rectangle on [0, 2]:

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The region between S and the t-axis on [0, 3] is a triangle:

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• The region between |x| and the x-axis on [-4, 3] consists of two triangles:

To find the value of the integral, we add the areas of the two triangles: