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If f(x) and g(x) are two real value functions such that∫ f(x)dx and∫ g(x)dx exist, then
Correct Answer Is : ∫k f(x)dx = k∫ f(x)dx If∫ f(x)dx = F(x), then∫ f (ax + b)dx = Correct Answer Is : 1/a F(ax + b) + c; a?0 Evaluate: ∫(3x + 4)^3 dx Correct Answer Is : (3x + 4)^4/12 Evaluate: ∫cos^3 x.dx Correct Answer Is : 3sin x /4 + 3sin 3x /12 + c True or false: if a and b are any non-zero real number,∫(e^(ax + b))dx=e^(ax + b) Correct Answer Is : FALSE Evaluate: ∫sin 7x.cos 3x.dx Correct Answer Is : (-cos 10x/20) - (cos4x/8) + c Integrate the function f(x) = (1/ 1 + cos x) with respect to x. Correct Answer Is : Tan x/2 + c Integrate the function f(x) = (tan x / sec x + tan x) with respect to x. Correct Answer Is : Sec x - tan x + x + c What are the different methods of integration? Correct Answer Is : All of these In which method, we reduced the given function to standard form by changing variable x to t, using some suitable substitution x = ∅(t). Correct Answer Is : Integration by substitution