solve this problem integration limit is 0 to 12 : (2x)dx-1
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∫₀¹² 2x dx / (x² + 1) = log(145)
Step-by-step explanation:
Now, ∫₀¹² 2x dx / (x² + 1)
= ∫₀¹² d(x² - 1) / (x² + 1)
= [ log(x² + 1) ]₀¹²
= log(12² + 1) - log(0² + 1)
= log(144 + 1) - log(0 + 1)
= log(145) - log(1)
= log(145) - 0
= log(145)
∴ ∫₀¹² 2x dx / (x² + 1) = log(145)
Integration:
Integration is a mathematical operation to find the function from it's derivatives. That's why we call it anti-differentiation.
If any function's derivative be f'(x), then it's integration with respect to x (for integration we take it as dx) be f(x) + c
We write it as
∫ f'(x) dx = f(x) + c , where c is integral constant
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