Question
Studdy Solution
STEP 1
1. The integral is a well-known Gaussian integral.
2. The integral does not have an elementary antiderivative.
3. The value of the integral can be determined using special techniques or known results.
STEP 2
1. Recognize the integral as a Gaussian integral.
2. Use the known result for the Gaussian integral over the entire real line.
3. Relate the given integral to the known result.
4. Calculate the value of the integral from to .
STEP 3
Recognize that the integral is related to the Gaussian integral .
STEP 4
Recall the known result for the Gaussian integral over the entire real line:
STEP 5
Since the function is even, the integral from to can be split into two equal parts:
STEP 6
Solve for the integral from to :
Divide both sides by 2:
The value of the integral is:
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