$\int_0^a f(x) \, dx = $

  • A
    $\int_0^a f(a + x) \, dx$
  • B
    $\int_0^a f(2a + x) \, dx$
  • C
    $\int_0^a f(x - a) \, dx$
  • D
    $\int_0^a f(a - x) \, dx$

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સંકલન $\sum\limits_{k = 1}^n {\int_0^1 {f(k - 1 + x)\,dx} } $ નું મૂલ્ય શું છે?

Difficult
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$\int_0^{\pi / 2} \log _e(\sin 2 x) d x$

$\int_{-1}^{0} \frac{4x^2 + 4x + 3}{1 + e^{2x + 1}} dx = $

જો $f(x) = \int_0^{\sin^2 x} \sin^{-1} \sqrt{t} \, dt$ અને $g(x) = \int_0^{\cos^2 x} \cos^{-1} \sqrt{t} \, dt$ હોય, તો $f(x) + g(x)$ ની કિંમત શોધો.

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