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If f, g are both continuous, and F, G are the primitive of f and g, then
∫f(t)g(t)dt\int_{ }^{ }f\left(t\right)g\left(t\right)dt∫f(t)g(t)dt =f(v)[∫g(t)dt]−∫ddvf(v)[∫g(t)dt]dvf\left(v\right)\left[\int_{ }^{ }g\left(t\right)dt\right]-\int_{ }^{ }\frac{d}{dv}f\left(v\right)\left[\int_{ }^{ }g\left(t\right)dt\right]dvf(v)[∫g(t)dt]−∫dvdf(v)[∫g(t)dt]dv
What is the name of this method?
Integration by substitution
Integration by parts
Which one is not method of integration?
Lebniz Rule
Which one is method of integration?
product rule
partial fraction
Which method is suitable to integrate: ∫1(4−x)2dx ?\int_{ }^{ }\frac{1}{\left(4-x\right)^2}dx\ ?∫(4−x)21dx ?
Which method is suitable to integrate:∫x3(x−2)(x+3)dx?\int_{ }^{ }\frac{x^3}{\left(x-2\right)\left(x+3\right)}dx?∫(x−2)(x+3)x3dx?
Evaluate:∫cos(x2)(2x)dx\int_{ }^{ }\cos\left(x^2\right)\left(2x\right)dx∫cos(x2)(2x)dx using substitution
xcosx−x+cx\cos x-x+cxcosx−x+c
sin(x2)+c\sin\left(x^2\right)+csin(x2)+c
2x−32x^{-3}2x−3
If f, g is both continuous, and F, G are the primitive of f and G, then
aF + bG = ∫(af+bg)\int_{ }^{ }\left(af+bg\right)∫(af+bg)
What is the name of this method for computing integrals?
linearity method
Evaluate:∫xsinxdx\int_{ }^{ }x\sin xdx∫xsinxdx integration by parts
−cosx+c-\cos x+c−cosx+c
−xcosx+sinx+c-x\cos x+\sin x+c−xcosx+sinx+c
Which method is suitable to integrate:∫1xlnxdx\int_{ }^{ }\frac{1}{x\ln x}dx∫xlnx1dx ?
It is done.