Question

$\int_{}^{}\sqrt{\frac{1–x}{1 + x}}$ dx =

• A. sin^–1 x – $\frac { 1 } { 2 }$ $\sqrt{1–x^{2}}$ + c
• B. sin^–1 x + $\frac{1}{2}\sqrt{1–x^{2}}$+ c
• C. sin^–1 x – $\sqrt{1–x^{2}}$ + c
• D. sin^–1 x + $\sqrt{1–x^{2}}$ + c

Answer 1

Answer: (B)

sin^–1 x + $\frac{1}{2}\sqrt{1–x^{2}}$+ c

Answer 2

dx , multiply and divide by

= $\int \frac { 1 - x } { \sqrt { 1 - x ^ { 2 } } }$ dx =

= sin^–1x + $\frac { 1 } { 2 }$dx

= sin^–1x + + c