The integration of a periodic function involves some unique properties and approaches due to the function’s repeating nature. A function $f(x)$ is said to be periodic with period $T$ if for all $x$ in the domain of $f$, $f(x + T) = f(x)$. This periodicity can significantly simplify the integration process over intervals that are […]
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This can be done in these simple steps
1) First draw a free body diagram of the body showing all the forces on it.
2) Carefully choose a X-Y coordinate system so that direction of the motion or direction of force lies in X or Y direction. This will simplfy the Problem
3) Applying Newton’s law find out any unknown forces
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For one dimensional motion, the force can be found from Potential energy using following formula
How to Calculate the force given potential energy Read More »
Two most common errors you should avoid when you see an average speed question.
Mistake #1
The most common mistakes in average speed problems occurs when the question asks you to calculate the average speed of a object moving at two different speeds for different parts of the journey. Students are generally tempted to calculate the arithmetic mean (average) of the two speeds, and select a corresponding answer. This averaging approach is wrong.
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Integration of sin square x can be calculated using trigonometric identities .Here is the formula for it $$ \int \sin^2(x) \, dx = \frac{1}{2} x – \frac{1}{4} \sin(2x) + C $$ Integration of sin 2x can be calculated using integration by substitutions .Here is the formula for it $$ \int \sin(2x) \, dx= \frac {-cos
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The integration of cot square x $\cot ^2 x$, can be found using trigonometry identities and fundamental integral formulas . The integral of $\cot^2 x$ with respect to (x) is: \[\int \cot^2 x \, dx =-\cot x -x + C\] Here, (C) represents the constant of integration, which is added because the process of integration
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The integration of tan square x $\tan ^2 x$, can be found using trigonometry identities and fundamental integral formulas . The integral of $\tan ^2 x$ with respect to (x) is: \[\int \tan^2 x \, dx =\tan x -x + C\] Here, (C) represents the constant of integration, which is added because the process of
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Acceleration Formula Acceleration is the rate of change of velocity with time. It is a measure of the change in the velocity of an object per unit time and mathematically acceleration formula is given as For describing average acceleration, we first consider the motion of an object along a straight line.Suppose at time t1 object is at
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