 # 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 Kye 2020-10-26 Answered
Convert the above indefinite integrals into definate integrals using the intervals $\left[0,1\right]$.
(a)$\int \sqrt{{a}^{2}-{x}^{2}}dx$
(b)$\int \sqrt{1-{x}^{2}}dx$
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Here instruction says only convert the indefinite integrals into definite integrals using the intervals $\left[0,1\right]$, 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 $\left[0,1\right]$, we use the concept
Integration of f(x) in the interval $\left[a,b\right]$
$\int f\left(x\right)dx,\left[a,b\right]$
${\int }_{a}^{b}f\left(x\right)$
a).
$\int \sqrt{{a}^{2}-{x}^{2}}dx,\left[0,1\right]$
Here upper limit is 1
and lower limit is 0
Definite integral is:
b).
$\int \sqrt{1-{x}^{2}}dx,\left[0,1\right]$
Here upper limit is 1
and lower limit is 0
Definite integral is:
${\int }_{0}^{1}\sqrt{1-{x}^{2}}dx$