MTH101 Quiz 2 Questions

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The volume of solid obtained when the region under the curve x=y over the interval [1,4] is revolved about the yaxis is V=∫14πy2dy

Zero The value of ∫12dx=

Let R be the plane region bounded above by a continuous curve y=f(x) below by the x-axis and on the left and right, respectively, by the lines x=a and x=b the volume of the solid generated by revolving R about the y-axis is given by ______. V=∫ab2πxf(x)dx The volume by the Washers generated by revolving the region around y-axis is given by the formula ---------- ∫abπ([u(y)]2+[v(y)]2)dy The method of slicing by integration is used for finding -

Volume

In order to fully determine the anti-derivative of a function f (F(x)), we must have..........

If the integral off(x) = x from x = 1 to x = 3 is 4, then the integral of f(x) = 10x from

x = 1 to x = 3 is ________.

IfF(x)istheanti−derivativeoff(x)on[a,b],i.eF/(t)=f(x),thenI fF(x)istheanti−derivativeoff(x)on[a,b],i.eF/(t)=f(x),then ∫baf(x)dx=F(b)−F(a)

Ifthecurveover[a,b]isrevolvedabouty−axis,thenthevolume iscalculatedbytheformula−−−−−−− ∫abπ[f(y)]2dy Integral of (1-2x) from [0,1] is ………..

The volume of the solid bounded by planes y=a and y=b with cross-sectional area A(y) perpendicular to the y-axis is V=∫abA(y)dyV=∫abA(y)dy First fundamental theorem of calculus gives the definite integral of a .......... function on a given closed interval in a quick way. Continuous x44−14=___ ∫1xt3dt We can break up definite integrals across a sum or difference ∫baf(x)±g(x)dx=∫abf(x)±g(x)dx= As ∫baf(x)dx±∫bag(x)dx∫abf(x)dx±∫abg(x)dx If the solid is revolved around the y-axis and generates a solid with a circular cross section of radius g(y) at y. Then the area of this cross section is π[g(y)]2π[g(y)]2 ∫abf(x)dx=______. −∫baf(x)dx−∫baf(x)dx

On that interval In integration of f(x)=x(x^2 +1)^3 from x=0 to x=2 by substitution method, we take u=x^2+1 then du=

2xdx