Convert the above indefinite integrals into definate integrals using the intervals [0,1]. (a)int sqrt(a^2-x^2)dx (b)int sqrt(1-x^2)dx

Convert the above indefinite integrals into definate integrals using the intervals [0,1]. (a)int sqrt(a^2-x^2)dx (b)int sqrt(1-x^2)dx

Question
Applications of integrals
asked 2020-10-26
Convert the above indefinite integrals into definate integrals using the intervals \(\displaystyle{\left[{0},{1}\right]}\).
(a)\(\displaystyle\int\sqrt{{{a}^{{2}}-{x}^{{2}}}}{\left.{d}{x}\right.}\)
(b)\(\displaystyle\int\sqrt{{{1}-{x}^{{2}}}}{\left.{d}{x}\right.}\)

Answers (1)

2020-10-27
Here instruction says only convert the indefinite integrals into definite integrals using the intervals \(\displaystyle{\left[{0},{1}\right]}\), so we will convert it only. If you want to solve it please submit your question with instruction.
Explanation:
To convert the indefinite integrals into definite integrals using the intervals \(\displaystyle{\left[{0},{1}\right]}\), we use the concept
Integration of f(x) in the interval \(\displaystyle{\left[{a},{b}\right]}\)
\(\displaystyle\int{f{{\left({x}\right)}}}{\left.{d}{x}\right.},{\left[{a},{b}\right]}\)
\(\displaystyle{\int_{{a}}^{{b}}}{f{{\left({x}\right)}}}\)
a).
\(\displaystyle\int\sqrt{{{a}^{{2}}-{x}^{{2}}}}{\left.{d}{x}\right.},{\left[{0},{1}\right]}\)
Here upper limit is 1
and lower limit is 0
Definite integral is:
b).
\(\displaystyle\int\sqrt{{{1}-{x}^{{2}}}}{\left.{d}{x}\right.},{\left[{0},{1}\right]}\)
Here upper limit is 1
and lower limit is 0
Definite integral is:
\(\displaystyle{\int_{{0}}^{{1}}}\sqrt{{{1}-{x}^{{2}}}}{\left.{d}{x}\right.}\)
0

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