Evaluate the definite integral. \int_{0}^{1}xe^{-x^{2}}dx

gainejavima 2021-11-22 Answered
Evaluate the definite integral.
01xex2dx
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Harr1957
Answered 2021-11-23 Author has 18 answers
Evaluate the definite integral.
01xex2dx
Let x2=t
2x dx=dt
xdx=dt2
01xex2dx=01etdt2
=1201etdt
=12[et]01
=12[e11]
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Warajected53
Answered 2021-11-24 Author has 12 answers
Step 1: Remove parentheses.
01xex2dx
Step 2: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:
abf(x)dx=F(x)ab=F(b)F(a)
Step 3: In this case, f(x)=xex2. Find its integral.
Step 4: Since F(x)ab=F(b)F(a), expand the above into F(1)−F(0):
e122(e022)
Step 5: Simplify.
e12+e02
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