difinite integral f(x)=1/y^2dy from x=1 to x=4
To find the definite integral of the function f(x) = 1/y^2 from x = 1 to x = 4, you need to follow these steps:
Step 1: Determine the antiderivative of the function f(x).
The antiderivative of f(x) = 1/y^2 is F(y) = -1/y.
Step 2: Evaluate the definite integral.
To evaluate the definite integral, substitute the upper and lower limits of integration into the antiderivative:
∫[1 to 4] (1/y^2) dy = F(4) - F(1)
= (-1/4) - (-1/1)
= -1/4 + 1
= 3/4.
Therefore, the value of the definite integral of f(x) from x = 1 to x = 4 is 3/4.