Evaluate the integral. \int_{0}^{2}\sqrt{4-x^{2}}dx

krypsojx

krypsojx

Answered question

2021-11-16

Evaluate the integral.
024x2dx

Answer & Explanation

Susan Yang

Susan Yang

Beginner2021-11-17Added 20 answers

Step 1
To evaluate: 024x2dx.
Solution:
We know that,
a2x2dx=12xa2x2+a22sin1xa+C
Using the above formula, we will evaluate the integral.
024x2dx=0222x2dx
=[12x22x2+222sin1(x2)]02
=[(1222222+2sin1(22))(0+2sin10)]
=[(0+2sin11)0]
2π2
=π
Step 2
Hence, required answer is π.
Clis1955

Clis1955

Beginner2021-11-18Added 9 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)=4x2. Find its integral.
4(sin1(x2)2+x1x244)02
Step 3: Since F(x)ab=F(b)F(a), expand the above into F(2)−F(0):
4(sin1(22)2+212244)4(sin1(02)2+010244)
Step 4: Simplify.
π

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