নির্দিষ্ট যোগজ
কোনো বক্ররেখার ঢাল tanx\tan{x}tanx হলে x=0x=0x=0 থেকে x=1x=1x=1 পর্যন্ত বক্ররেখাটির দৈর্ঘ্য কত হবে?
2.339
1.226
1.991
3
y=∫tanx dx=ln(secx)+c ;ds2=dx2+dy2y=\int{\tan{x}\ dx=\ln{(\sec{x}})+c}\ ;ds^2=dx^2+dy^2y=∫tanx dx=ln(secx)+c ;ds2=dx2+dy2
⇒ds=1+(dydx)2dx⇒∫0sds=∫011+tan2xdx⇒s=∫01secx dx=1.226\Rightarrow ds=\sqrt{1+\left(\frac{dy}{dx}\right)^2}dx\Rightarrow\int_{0}^{s}{ds=}\int_{0}^{1}{\sqrt{1+\tan^2{x}}dx}\Rightarrow s=\int_{0}^{1}{\sec{x\ dx}=1.226}⇒ds=1+(dxdy)2dx⇒∫0sds=∫011+tan2xdx⇒s=∫01secx dx=1.226
∫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?
∫oπ2dx1+cosx=? \int_{o}^{\frac{\pi}{2}} \frac{dx}{1 + \cos{x}} = ? ∫o2π1+cosxdx=?
