Question

f=__dx____ =
√(1-2)(x-2)
a) sin^-1(3-2x)+c
b)sin^-1(5-2x)+c
c)sin^-1(2x-3)+c
d)sin^-1(2x+5)+c

This is an Indefinite Integration of 12th science please help me​

Answer 1

Answer:

sin^(-1) (2x - 3) + C

Step-by-step explanation:

Integration of the given f(x) :

=> dx

√(1-x)(x-2)

=> dx

√(3x-2-x²)

=> dx

√(-2-x²+3.2(x/2)+3²/2²-3²/2²))

=> dx

√(9/4 -2 - (x-3/2)²)

=> dx

√(1/2² - (x-3/2)²)

Let x - 3/2 = t => dx = dt

=> dt

√(1/2² - t²)

=> sin^(-1) (t/(1/2)) + C => sin^(-1) (2t) + C

=> sin^(-1) (2x - 3) + C