_ a-6 ^ b-6 f(x + 6) ,dx is equal to

Step-by-step solution

Let t = x + 6 . Differentiating both sides with respect to x , we get dt = dx . When x = a - 6 , t = a - 6 + 6 = a . When x = b - 6 , t = b - 6 + 6 = b . Substituting these into the integral, we get: _ a-6 ^ b-6 f(x + 6) , dx = _ a ^ b f(t) , dt Using the property of definite integrals _ a ^ b f(t) , dt = _ a ^ b f(x) , dx , we get: _ a ^ b f(x) , dx Answer: _ a ^ b f(x) ,dx