Blank notes

1. 1
MAT 241 Section 5.6 Definite Integral Substitutions and the Area Between Curves
Example 1. Evaluate the definite integral.
1
2 4
0
2 ( 1)x x dx+

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Example 1. Evaluate the definite integral.
1
2 4
0
2 ( 1)x x dx+

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Example 2. Evaluate the definite integral.
2
0
2 x dx−

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Example 3. Evaluate the definite integral.
/4
4 2
0
tan secx xdx



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Example 4. Evaluate the definite integral.
3
2
1
4(ln )x
dx
x

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Example 5. Evaluate the definite integral.
0
sin
2 cos
x
dx
x

−

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Areas Between Curves

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Example 6. Find the area bounded by the graphs given by the equations.
2
5 andy x x y x= − =

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Example 7. Find the area bounded by the graphs given by the equations.
3
and 4y x y x= =

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Example 8. Integrating with respect to y.
Find the area bounded by the graphs given by the equations.
2 andy x y x= + =