Use the form of the definition of the integral given in Theorem 4 to evaluate...

David Troyer

David Troyer

Answered

2021-12-16

Use the form of the definition of the integral given in
Theorem 4 to evaluate the integral.
02(2xx3)dx

Answer & Explanation

temzej9

temzej9

Expert

2021-12-17Added 30 answers

Step 1
To evaluate the integral: 02(2xx3)dx
Evaluating the integral.
02(2xx3)dx=022xdx02x3dx
=(2x22)02(x44)02
=(x2)02(2240)
=(4-0)-(1-0)
=4-1
=3
Step 2
Hence, required answer is 3.
levurdondishav4

levurdondishav4

Expert

2021-12-18Added 38 answers

(2xx3)dx
Lets
nick1337

nick1337

Expert

2021-12-28Added 573 answers

We represent the original integral as a sum of tabular integrals:
(2xx3)dx=x3dx+2xdx
(x3)dx
This is a tabular integral:
x3dx=x44+C
2xdx
This is a tabular integral:
2xdx=x2+C
(2xx3)dx=x44+x2+C
Let's calculate the definite integral:
02(2xx3)dx=(x44+x2)02
F(2)=0
F(0)=0
I=0-(0)=0

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