Question

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Explain the rules of integration
Class 11 Physics .......


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Answer 1

Example: What is ∫x3 dx ?

The question is asking "what is the integral of x3 ?"

We can use the Power Rule, where n=3:

∫xn dx = xn+1n+1 + C

∫x3 dx = x44 + C

Example: What is ∫√x dx ?

√x is also x0.5

We can use the Power Rule, where n=½:

∫xn dx = xn+1n+1 + C

∫x0.5 dx = x1.51.5 + C

Multiplication by constant

Example: What is ∫6x2 dx ?

We can move the 6 outside the integral:

∫6x2 dx = 6∫x2 dx

And now use the Power Rule on x2:

= 6 x33 + C

Simplify:

= 2x3 + C

Sum Rule

Example: What is ∫cos x + x dx ?

Use the Sum Rule:

∫cos x + x dx = ∫cos x dx + ∫x dx

Work out the integral of each (using table above):

= sin x + x2/2 + C

Difference Rule

Example: What is ∫ew − 3 dw ?

Use the Difference Rule:

∫ew − 3 dw =∫ew dw − ∫3 dw

Then work out the integral of each (using table above):

= ew − 3w + C