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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

Example 1

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(x) = 10x9

Example 2

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(x) = x3

Example 3

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

Example 4

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(t) = -sin t

Example 5

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(x) = -cos x

Example 6

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(t) = sec2 t

Example 7

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(x) = e2x

Example 8

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(x) = 5x ln 5

Example 9

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

Example 10

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

f(x) = x2 + 3x – 5

Example 11

Evaluate the integral.

Example 12

Evaluate the integral.

Example 13

Evaluate the integral.

Example 14

Evaluate the integral.

Example 15

Evaluate the integral.

Example 16

Evaluate the integral.

Example 17

Evaluate the integral.

Example 18

Evaluate the integral.

Example 19

Evaluate the integral.

Example 20

Evaluate the integral.

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