Question

solve this problem integration limit is 0 to 12 : (2x)dx-1​

Answer 1

∫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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Answer 2

Answer:

Step-by-step explanation: