Evaluate the following iterated integrals. int_1^2int_0^1(3x^2+4y^3)dydx

shadsiei 2021-01-10 Answered
Evaluate the following iterated integrals.
1201(3x2+4y3)dydx
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Expert Answer

irwchh
Answered 2021-01-11 Author has 102 answers
To evaluate the integral: 1201(3x2+4y3)dydx
Solution:
When we integrate with respect to one variable then other will be kept as constant.
Evaluating the integral.
1201(3x2+4y3)dy=12[01(3x2+4y3)dy]dx
=12[(3x2y+4y44)01]dx
=12[3x21+140]dx
=12(3x2+1)dx
=[3x33+x]12
=[x3+x]12
=[(23+2)(13+1)]
=[122]
=10
Hence, required answer is 10
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