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Example Questions
Example Question #141 : Definite Integrals
Evaluate .
The integral cannot be evaluated.
This integral cannot be evaluated using the Fundamental Theorem of Calculus, since an antiderivative does not exist for . Instead, we need to find the area under the curve
bounded by the
axis.
from
, is the graph of the upper half of the circle
. The area of this upper half is
.
Hence .
Example Question #142 : Definite Integrals
First, chop up the fraction into two separate fractions:
Now, integrate:
Next, evaluate at 2 and then at 0. Subtract the results:
.
Example Question #143 : Definite Integrals
First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:
Simplify to get:
Now, evaluate at 3 and then at 1. Subtract the results:
Example Question #151 : Finding Integrals
First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:
Simplify to get:
Now, evaluate at 3 and then 0. Subtract the results:
Example Question #2252 : Calculus Ii
First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:
Now, evaluate at 2 and then 1:
.
Example Question #152 : Finding Integrals
Recall that when integrating, you must raise the exponent by 1 and also put that result on the denominator:
Simplify to get:
Now, evaluate at 1 and then at 0:
Example Question #142 : Definite Integrals
First, integrate. Remember to raise the exponent by 1 and then also put that result on the denominator:
Next, evaluate at 2 and then 1. Subtract the results:
Simplify:
Example Question #162 : Finding Integrals
First, chop up the fraction into two separate terms:
Now, integrate:
Now, evaluate at 4 and then 0. Subtract the results:
Example Question #512 : Integrals
First, integrate. Remember to add one to the exponent and then also put that result on the denominator:
Now, evaluate at 3 and then 1. Subtract the results:
Simplify:
Example Question #142 : Definite Integrals
First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:
Now, evaluate at 2 and then 1:
Simplify to get your answer:
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