\(\int tan(x)dx
\\tan(x)=\frac{sin(x)}{cos(x)}
\\\Rightarrow \int tan(x)=\int \left ( \frac{sin(x)}{cos(x)} \right )dx\)
Let t=cos(x)
\(\\\Rightarrow\frac{dt}{dx} =\frac{d}{dx}cos(x)=-sin(x)
\\\Rightarrow dx=-sin(x)dt
\\= -\int \frac{1}{t}dt
\\=-ln\left | t \right |+C\)
On putting the value of ‘t’
\(\\=-ln\left | cos(x) \right |+C\)
Two spaceships are moving towards each other at a speed of 0.5c relative to the galaxy. Spaceship A sends an emergency signal to spaceship B with a frequency f = 20GHz.
When exploring a small planet with a radius of 770 km and a mass of 8.48 x 10^30 kg a small spacecraft with a mass of 8170 kg is placed in an elliptical orbit around it.
The Cessna Cardinal, a single-engine light airplane, has a wing with an area of 16.2 m2 and an aspect ratio of 7.31. Assume that the span efficiency factor is 0.62.
Investigate the principles of aerodynamics in mechanical engineering, covering topics such as fluid flow around objects, lift and drag forces, and boundary layer phenomena.
Consider an airplane in an accelerated climb. At a given instant in this climb, the specific excess power is 120 ft/s
