Important Short Questions for Chatper 03

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Fsc part 02

Important Short Questions for Chatper 03


Find \partial{y} and dy if y=x^2-1 when x changes from 3 to 3.02
Find \partial{y} and dy if y=\sqrt{x} when x changes from 4 to 4.41
Find approximate increasse in the volume of a cube if the length of its each edge changes from 5 to 5.02
Evaluate \int{x(\sqrt{x}+1)dx}
Evaluate \int{ (2x+3)^\frac{1}{2} dx}
Evaluate \int{(\sqrt{x}+1)^2 dx}
Evaluate \int{\frac{(3x+2)}{\sqrt{x}} dx}
Evaluate \int{\frac{(\sqrt{θ}-1)^2}{\sqrt{θ}} dθ}
Evaluate \int{\frac{(1-\sqrt{x})^2}{\sqrt{x}} dx}
Evaluate \int{(a-2x)^{\frac{3}{2}} dx}
Evaluate \int{\sqrt{1-cos2x} dx }
Evaluate \int{(lnx)× \frac{1}{x} dx}
Evaluate \int{\frac{1}{1+cosx} dx}
Evaluate \int{cos3x sin2x dx}
Evaluate \int{tan^{2}⁡x dx}
Evaluate \int{\frac{x}{\sqrt{4+x^2 }} dx}
Evaluate \int{\frac{x^2}{4+x^2 } dx}
Evaluate \int{\frac{dx}{x^2+4x+13}}
Evaluate \int{\frac{1}{xlnx} dx}
Evaluate \int{\frac{sec^2⁡x}{\sqrt{tanx}} dx}
Evaluate \int{sin^{2}⁡x dx}
Evaluate \int{\frac{1}{(1+x^2 )} tan^{-1}⁡x dx}
Evaluate \int{\frac{sinθ}{1+cos^{2⁡}θ } dθ}
Evaluate \int{cosx\frac{(ln sinx)}{sinx} dx}
Evaluate \int{\frac{ \sqrt{2}{sinx+cosx} dx}
Evaluate \int{xcosx dx}
Evaluate \int{lnx dx}
Evaluate \int{x lnx dx}
Evaluate \int{tan^{-1}⁡x dx}
Evaluate \int{x^2 sinx dx}
Evalluate \int{x tan^{-1}{⁡x} dx}
Evaluate \int{e^x (\frac{1}{x}+lnx)dx }
Evaluate \int{e^x (cosx+sinx) dx }
Evaluate \int{e^{2x} (-sinx+2cosx)dx}
Evaluate \int{e^{-x} (cosx-sinx)dx}
Evaluate \int{\frac{e^{mtan^{-1} x}}{1+x^2} dx}
Evaluate \int_{-1}^{3}({x^3+3x^2})dx

Evaluate\int_{-1}^{2}{(x+|x|)}dx
Evaluate\int_{1}^{e}{x lnx} dx
Evaluate\int_{-1}^{1}{(x^\frac{1}{3}+1)}dx
Evaluate\int_{-2}^{0}{\frac{1}{(2x-1)^2}} dx
Evaluate\int_{-6}^{2}{ \sqrt{3-x}} dx
Evaluate\int_{2}^{ \sqrt{5}}{x \sqrt{x^2-1}} dx
Evaluate\int_{1}^{2}{\frac{x}{x^2+2}} dx
Evaluate\int{0}^{3}{\frac{dx}{x^2+9}
Evaluate\int_{1}^{2}{lnx} dx
Evaluate\int_{0}^{2}{e^{\frac{x}{2}}-e^-{\frac{x}{ 2}} }dx
Evaluate\int{0}^{\frac{π}{3}}{cos^2⁡θ dθ}
Evaluate\int_{-1}^{5}{|x-3| } dx
Evaluate\int_{\frac{1}{8}}^{1}{\frac{(x^{\frac{1}{3}}+2)^2}{x^{\frac{2}{3}}}} dx
Evaluate\int_{0}^{\frac{π}{4}}{\frac{sinx-1}{cos^2⁡x}} dx

Find the area between the x-axis and the curve y=4x-x^2
Solve the differential equation \frac{dy}{dx}=\frac{1-x}{y}
Solve the differential siny cosecx \frac{dy}{dx}=1
Solve the differential equation \frac{1}{x}\frac{ dy}{dx}-2y=0

Importan short Questions for chap # 02 click here

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