3
⌠
2⌡ (2x^2+5) / x^2 dx =?
I got 1.66 but it was wrong.
That's supposed to be an integral sign.
First separate it into
3
⌠
2⌡(2x^2/x^2) dx +
3
⌠
2⌡ 5x^-2 dx = ........
I'm sure you can continue the process. The answer is 17/6
To solve this definite integral, you can follow these steps:
Step 1: Distribute the numerator if necessary.
(2x^2 + 5)/x^2 = 2(x^2)/x^2 + 5/x^2 = 2 + 5/x^2
Step 2: Simplify the integral.
∫[a to b] (2 + 5/x^2) dx
Step 3: Integrate term by term.
∫[a to b] 2 dx + ∫[a to b] 5/x^2 dx
Step 4: Evaluate the definite integral.
∫[a to b] 2 dx = 2x ∣[a to b] = 2b - 2a
∫[a to b] 5/x^2 dx = -5/x ∣[a to b] = (-5/b) - (-5/a) = 5(1/b - 1/a)
Step 5: Combine the results.
∫[a to b] (2 + 5/x^2) dx = (2b - 2a) + 5(1/b - 1/a)
Since you did not provide the limits of integration (a and b), I cannot calculate the final result. Make sure to substitute the appropriate values of a and b to get the correct answer.