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Math 110 Course Resources
- Definite Integrals Course Packet on the Fundamental Theorem of Calculus
Compute the area of the region under the graph of from to .
Area
Studdy Solution
STEP 1
1. We are given a definite integral to evaluate.
2. The function to integrate is .
3. The limits of integration are from to .
4. The problem requires the use of basic integration techniques and the Fundamental Theorem of Calculus.
STEP 2
1. Simplify the integrand.
2. Integrate the simplified function.
3. Evaluate the definite integral using the limits of integration.
STEP 3
Simplify the integrand .
Rewrite the expression as two separate terms:
Simplify each term:
STEP 4
Integrate the simplified function .
The antiderivative of is:
The antiderivative of is:
Combine the antiderivatives:
STEP 5
Evaluate the definite integral from to .
Substitute the upper limit into the antiderivative:
Calculate each term:
Substitute the lower limit into the antiderivative:
Subtract the lower limit evaluation from the upper limit evaluation:
The value of the definite integral is:
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