Math Problem Statement
Evaluate R 2 0 xex 2 dx.
Solution
To evaluate the integral , we can use the technique of substitution.
Step 1: Substitution
Let . Then, the derivative of with respect to is: So, , or .
Step 2: Rewrite the Integral
Substitute into the integral: Given , when , , and when , . Therefore, the integral becomes:
Step 3: Evaluate the Integral
The integral of with respect to is simply . So, we have:
Step 4: Simplify the Result
Since , the final expression is:
So, the evaluated integral is:
Would you like more details or have any questions?
Related Questions:
- How would the integral change if the limits were different, say from 1 to 3?
- Can the method of integration by parts be applied to this integral?
- How does substitution work in integrals involving trigonometric functions?
- What is the significance of the constant factor in definite integrals?
- How does the exponential function behave under integration compared to polynomial functions?
Tip: Substitution is a powerful technique for solving integrals where the integrand is a composite function, especially when one part of the function is the derivative of another.
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Math Problem Analysis
Mathematical Concepts
Integration
Substitution
Exponential Functions
Formulas
Substitution in integrals
Theorems
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Suitable Grade Level
Advanced High School to College