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Suppose we are required to find the difference between 3abc and 7abc. We look at two scenarios. The value we would obtain by subtracting a larger quantity from the smaller quantity is not the same as one got by subtracting the lower value from the higher value. In the first scenario we have 7abc - 3abc which is 4abc. This is different from the value got in the second scenario which is 3abc - 7abc = - 4abc. Therefore, whenever a bigger value is subtracted from a smaller value, the process is as usual but to the solution part we prefix the minus sign, while the subtraction of a smaller value from a bigger value is nothing but the normal subtraction.
Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on
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Evaluate following integrals. (a) ∫ 3e x + 5 cos x -10 sec 2 x dx (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a) ∫ 3e x + 5 cos x -10 sec 2 x
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