WebApr 28, 2024 · Here R.H.S. of the equation means integral of f(x) with respect to x, F(x) is called anti-derivative or primitive, f(x) is called the integrand, dx is called the integrating agent, C is called constant of integration or arbitrary constant and x is the variable of integration. ... ∫ cosec 2 x dx = -cot x + C; ∫ sec x tan x dx = sec x + C ... WebNov 26, 2016 · ∫ c o s e c ( 2 x) d x = ∫ 1 + t a n 2 x 2 t a n ( x) d x Now put t = t a n ( x) d t = ( s e c 2 x) d x = ( 1 + t a n 2 x) d x = ( 1 + t 2) d x Hence the integral becomes ∫ 1 + t 2 2 t × d t 1 + t 2 Can you complete the solution? Share Cite Follow edited Nov 26, 2016 at 9:49 answered Nov 26, 2016 at 9:22 Shraddheya Shendre 2,421 1 16 32
Trigonometric Functions - Formulas, Graphs, Examples, Values / …
WebThe integral of cosec x is denoted by ∫ cosec x dx (or) ∫ csc x dx and its value is ln cosec x - cot x + C. This is also known as the antiderivative of cosec x. We have multiple formulas for this. But the more popular formula is, ∫ cosec x dx = ln cosec x - cot x + C. WebApr 12, 2024 · Sum Rule of Integration. In accordance with the sum rule of integration, integrating the sum of two functions is equal to the sum of the integral of each function. ∫ (f + g) dy = ∫f dy + ∫g dy. Example: ∫ (y + y 3 )dy. = ∫y dy + ∫y 3 dy. = y 2 /2 + y 4 /4 + C. Introduction to Integrals Detailed Video Explanation. qual a mais alta montanha na ásia yytyyyy
All Integration Formulas- PDF, List, Sheet for Class 12 - adda247
WebThe integration of cosec inverse x or arccosec x is x c o s e c − 1 x – l o g x – x 2 – 1 + C Where C is the integration constant. i.e. ∫ c o s e c − 1 x = x c o s e c − 1 x – l o g x – x 2 – 1 + C Proof : We have, I = ∫ c o s e c − 1 x dx Let c o s e c − 1 x = t, Then, x = cosec t dx = d (cosec t) = -cosec t cot t dt WebOct 11, 2024 · Some of the important integration formulas of trigonometric functions are listed below: ∫ s i n ( x) d x = − c o s ( x) + C ∫ c o s ( x) d x = s i n ( x) + C ∫ t a n ( x) d x = l n s e c ( x) + C ∫ s e c ( x) d x = l n t a n ( x) + s e c ( x) … WebOct 20, 2016 · Explanation: If we want to derive the reduction formula: I = ∫cscn(x)dx = ∫cscn−2(x)csc2(x)dx Now, perform integration by parts on this, taking the form ∫udv = uv − ∫vdu. Let u = cscn−2(x). Differentiating this gives: du = (n − 2)cscn−3(x) ⋅ ( − csc(x)cot(x))dx du = −(n −2)cscn−2(x)cot(x)dx And let dv = csc2(x). Integrating this gives v = −cot(x). haus toskana kaufen meerblick