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integration

Integration By Substitution – Formula and Examples

Here you will learn what is integration by substitution method class 12 with examples. Let’s begin – Integration By Substitution The method of evaluating an integral by reducing it to standard form by a proper substitution is called integration by substitution. If ϕ(x) is continuously differentiable function, then to evaluate integrals of the form […]

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What is walli’s formula in integration ?

Walli’s Formula : If m,n N & m, n 2, then (a)  π/20 sinnxdx = π/20 cosnxdx = (n1)(n3).(1or2)n(n2).(1or2) K where K = {π/2if n is even 1if n is odd  (b)  sinnx.cosmxdx = \([(n-1)(n-3)….(1 or 2)][(m-1)(m-3)….(1 or 2)]\over {(m+n)(m+n-2)(m+n-4)….(1 or

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What is Newton Leibnitz formula with Examples ?

Newton Leibnitz formula If h(x) and g(x) are differentiable functions of x then, ddx h(x)g(x) f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x) Example : Evaluate ddt t3t2 1logx dx Solution : We have, ddt t3t2 1logx dx = 1logt3 ddt (t3)1logt2 ddt

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Integration of Sec Inverse x and Cosec Inverse x

Here you will learn proof of integration of sec inverse x  and cosec inverse x. Let’s begin – Integration of Sec Inverse x The integration of sec inverse x or arcsec x is xsec1xlog|x+x21| + C Where C is the integration constant. i.e. sec1x = xsec1x – \(log|x

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