Evaluate the definity integral. int_{0}^{4}(x-3)(x-5)dx

jeliceg2

jeliceg2

Answered question

2021-11-22

Evaluate the definity integral.
04(x3)(x5)dx

Answer & Explanation

Mollicchiuk

Mollicchiuk

Beginner2021-11-23Added 13 answers

Step 1
Evaluate the integral 04(x3)(x5)dx.
Step 2
04(x3)(x5)dx=04x28x+15dx
=(x334x2+15x)04
=(43343+15×4)
=523
John Timms

John Timms

Beginner2021-11-24Added 8 answers

Step 1: 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 2: In this case, f(x)=(x-3)(x-5). Find its integral.
x334x2+15x04
Step 3: Since F(x)ab=F(b)F(a), expand the above into F(4)−F(0):
(4334×42+15×4)(0334×02+15×0)
Step 4: Simplify.
=523

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