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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
$\frac{d}{dx}\left[\int_{0}^{2a} f(\sin 2x)\,dx\right] =$
Solution
Given solution:
$y = e^x (a\cos x + b\sin x)$
Here the solution contains **two arbitrary constants** $a$ and $b$.
The order of a differential equation is equal to the number of arbitrary constants in its general solution.
Therefore,
Observe that the integral
$\int_{0}^{2a} f(\sin 2x)\,dx$
does **not depend on $x$** because the limits are constants.
Hence the entire expression is a constant.
Derivative of a constant is zero.
Therefore,
$\frac{d}{dx}\left[\int_{0}^{2a} f(\sin 2x)\,dx\right] = 0$
Order $=2$
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