Definite Integration – Mathemerize

What is walli’s formula in integration ?

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Walli’s Formula : If m,n $\in$ N & m, n $\ge$ 2, then (a) $\int_{0}^{\pi/2}$ $sin^nx$ dx = $\int_{0}^{\pi/2}$ $cos^nx$ dx = $(n-1)(n-3)….(1 or 2)\over {n(n-2)….(1 or 2)}$ K where K = $\begin{cases} \pi/2 & \text{if n is even}\ \\ 1 & \text{if n is odd}\ \end{cases}$ (b) $sin^nx.cos^mx$ dx = \([(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 ?

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Newton Leibnitz formula If h(x) and g(x) are differentiable functions of x then, $d\over dx$ $\int_{g(x)}^{h(x)}$ f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x) Example : Evaluate $d\over dt$ $\int_{t^2}^{t^3}$ $1\over log x$ dx Solution : We have, $d\over dt$ $\int_{t^2}^{t^3}$ $1\over log x$ dx = $1\over log t^3$ $d\over dt$ $(t^3)$ – $1\over log t^2$ $d\over dt$

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Integration Examples

Here you will learn some integration examples for better understanding of integration concepts. Example 1 : Evaluate : $\int$ $dx\over {3sinx + 4cosx}$ Solution : I = $\int$ $dx\over {3sinx + 4cosx}$ = $\int$ $dx\over {3[{2tan{x\over 2}\over {1+tan^2{x\over 2}}}] + 4[{1-tan^2{x\over 2}\over {1+tan^2{x\over 2}}}]}$ = $\int$ $sec^2{x\over 2}dx\over {4+6tan{x\over 2}-4tan^2{x\over 2}}$ let $tan{x\over 2}$ =

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Properties and Formulas for Definite Integrals

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Here, you will learn formulas for definite integrals and properties of definite integrals with examples. Let’s begin – A definite integral is denoted by $\int_{a}^{b}$ f(x)dx which represent the algebraic area bounded by the curve y = f(x), the ordinates x = a, x = b and the x-axis. Properties and Formulas for Definite Integrals

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