show that the area under the force time graph gives the magnitude of the impulse of the given force for the following case: 
​(A)constant force
(B)variable force

Dear Student ,
The area under the force time graph is the product of force and time .
Again the impulse of force is P = Force $\times$ time .
Now for both the variable force and constant force the force-time graph is shown here below.
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Now for the constant force the impulse is the area OABD and in case of variable force is the sum of the area of OHAE,EABI,IBCF,FCDG .
Regards