Question

what was the integration of√1-4x^2​

Answer 1

Answer:

1/4[(sin-¹(2x)+(2x)(√1-4x²)]

Step-by-step explanation:

√1-(2x)²

let 2x=sinq

q=sin-¹(2x)

so 2dx=cosq

dx=cosq/2 dq

now √1-(2x)²=√1-sin²q=cosq

now

int of cosq.cosq/2 dq

int of cos²q/2 dq

1/2 int of cos²q dq

1/2 int of 1/2(1+cos2q)dq

1/4[q+(sin2q/2)]

while

sin2q/2=2sinqcosq/2=sinqcosq

now sinq=2x and cosq=√1-4x²

so

ans will be

1/4[(sin-¹(2x)+(2x)(√1-4x²)]