MCQ
$\int_{}^{} {{e^{2x}}( - \sin x + 2\cos x)\;dx = } $
- A${e^{2x}}\sin x + c$
- B$ - {e^{2x}}\sin x + c$
- C$ - {e^{2x}}\cos x + c$
- ✓${e^{2x}}\cos x + c$
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$(i)$ $f (x)$ is bounded on $a \le x \le b.$
$(ii)$ The equation $f (x) = 0$ has at least one solution in $a < x < b.$
$(iii)$ The maximum and minimum values of $f (x)$ on $a \le x \le b$ occur at points where $f ' (c) = 0$.
$(iv)$ There is at least one point $c$ with $a < c < b$ where $f ' (c) > 0$.
$(v)$ There is at least one point $d$ with $a < d < b$ where $f ' (c) < 0.$