1 / 10
00
Which one is method of integration?
Lebniz Rule
product rule
partial fraction
Integration by substitution
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 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 parts
Which method is suitable to integrate:∫1xlnxdx\int_{ }^{ }\frac{1}{x\ln x}dx∫xlnx1dx ?
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
Which method is suitable to integrate: ∫1(4−x)2dx ?\int_{ }^{ }\frac{1}{\left(4-x\right)^2}dx\ ?∫(4−x)21dx ?
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 one is not method of integration?
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?
It is done.