intergrate bound is 4 and 1 equation is xrootx dx
To calculate the definite integral of x√x from 1 to 4, we can use the following steps:
1. Rewrite the integral as x^(3/2).
2. Integrate x^(3/2) with respect to x:
∫ x^(3/2) dx = (2/5)x^(5/2) + C
3. Evaluate the antiderivative at the upper and lower bounds:
[(2/5)(4)^(5/2) - (2/5)(1)^(5/2)]
4. Simplify the expression:
= (2/5)(32) - 2/5
= (64/5) - (2/5)
= 62/5
Therefore, ∫ from 1 to 4 of x√x dx = 62/5.