Topic
Q:
a) \( \int_{0}^{2} \sqrt{\tan \theta} d \theta \),
Q:
\( f(x)=\left\{\begin{array}{lll}x^{2}-1 & \text { for } & x<1 \\ x^{2}+1 & \text { for } & x \geq 1\end{array}\right\} \) at \( x=1 \)
Q:
a) \( \int_{0}^{+\infty} x^{a} e^{-x^{b}} d x=\frac{1}{b} \Gamma\left(\frac{a+1}{b}\right) \quad(a>-1, b>0 \)
Q:
\( \operatorname { im } _ { x \rightarrow 0 } ( ( \sin ( x ) ) ^ { 2 } \times \sin ( \frac { 1 } { x } ) ) \ldots \)
Q:
Encuentre el área encerrada entre las funciones \( y = \frac{x}{2} + 3 \) y \( y = x^2 + 1 \) en el intervalo \( [0,3] \).
Q:
Calculate the volume obtained by revolving the area between \( y = \frac{1}{x} \), \( y = 0 \), and \( x = 1 \) to \( x = 2 \) around the y-axis using the disc method.
Q:
\( \int _{}^{}\frac{1}{2}\sin (x)^{2} d x \)
Q:
\( \lim _ { x \rightarrow 0 ^ { + } } ( \sin 2 x ) . \)
Q:
Q. 31. Prove that :
\[ \begin{array}{l}\text { logsec } x=\frac{x^{2}}{2}+\frac{x^{4}}{12}+\frac{x^{6}}{45}+\ldots \\ \text { (Rewa 1992, 2001, 19; Gwalior }\end{array} \]
Q:
(c) \( \int e^{x} \operatorname{ch} x d x \)
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