নির্দিষ্ট যোগজ
∫−11ex1+2ex \int_{-1}^{1} \frac{e^{x}}{1+2 e^{x}} ∫−111+2exex মান কত?
ln(1+e)
12ln(1+2e)(1+2e)
13ln(1+3e)
none of these
let,
1+2ex=t⇒2ex=t \begin{aligned} 1+2 e^{x} & =t \\ \Rightarrow 2 e^{x} & =t\end{aligned} 1+2ex⇒2ex=t=t
∫−11ex1+2ex=∫12tdt \begin{array}{l}\int_{-1}^{1} \frac{e^{x}}{1+2 e^{x}} \\ =\int \frac{1}{2} t d t\end{array} ∫−111+2exex=∫21tdt
=12∫1tdt⇒12lnt=12[ln(1+2ex)]−11 =\frac{1}{2} \int \frac{1}{t} d t \Rightarrow \frac{1}{2} \ln t=\frac{1}{2}\left[\ln \left(1+2 e^{x}\right)\right]_{-1}^{1} =21∫t1dt⇒21lnt=21[ln(1+2ex)]−11
=12ln(e+2e2e+2) =\frac{1}{2} \ln \left(\frac{e+2 e^{2}}{e+2}\right) =21ln(e+2e+2e2)
∫0π4cosθcos2θdθ=? \int_{0}^{\frac{\pi}{4}} \frac{\cos \theta}{\cos ^{2} \theta} d \theta=? ∫04πcos2θcosθdθ=?
∫0π2cos3xsinxdx \int_{0}^{\frac{\pi}{2}} \cos ^{3} x \sqrt{\sin x} d x ∫02πcos3xsinxdx
The value of ∫−π/2199π/2(1+cos2x)dx\displaystyle\int^{199\pi/2}_{-\pi/2}\sqrt{(1+\cos 2x)}dx∫−π/2199π/2(1+cos2x)dx is?
∫0π4cos2θcos2θ=?\int_0^{\frac{\pi}{4}} \frac{cos 2 \theta}{cos² \theta} = ? ∫04πcos2θcos2θ=?
