# Unit 03: Integration

Here is the list of important questions.

• Evaluate $\int \frac{1}{\sqrt{x}(\sqrt{x}+1)}dx$ — BSIC Gujranwala (2016)
• Find $\int \frac{1}{1+ cosx}dx$ — BSIC Gujranwala (2016)
• Evaluate $\int \frac{1}{x \ln x}dx$ — BSIC Gujranwala (2016)
• Find $\int x \ln x dx$ — BSIC Gujranwala (2016)
• Evaluate $\int e^{2x}(-sinx+2cosx)dx$ — BSIC Gujranwala (2016)
• Compute $\int^2_1(x^2+1)dx$— BSIC Gujranwala (2016)
• Calculate $\int^{\frac{\pi}{4}}_0 \sec x(\sec x+\tan x)dx$— BSIC Gujranwala (2016)
• Solve the differential equation $\sin y cosec x \frac{dy}{dx}=1$ — BSIC Gujranwala (2016)
• Evaluate $\int \sqrt{4-5x^2}dx$ — BSIC Gujranwala (2016)
• Evaluate $\int ^3_{-1}(x^3+3x^2)dx$ — BSIC Gujranwala (2016)
• Evaluate $\int (a-2x)^{\frac{3}{2}}dx$ — BSIC Gujranwala (2015)
• Evaluate $\int \sqrt{1+\sin x}dx$ — BSIC Gujranwala (2015)
• Evaluate $\int \frac{1}{a^2-X^2}dx$ — BSIC Gujranwala (2015)
• Evaluate $\int \frac{e^{mtan^{-1}x}}{1+x^2}dx$ — BSIC Gujranwala (2015)
• Find $\int x e^xdx$ — BSIC Gujranwala (2015)
• Find area between $x-axis$ and the curve $y=\sin 2x$ from $x=0$ to $x=\frac{\pi}{3}$ — BSIC Gujranwala (2015)
• Solve $\frac{dy}{dx}+\frac{2xy}{2y+1}=x$ — BSIC Gujranwala (2015)
• Evaluate $\int ^2_{-1}\ln xdx$ — BSIC Gujranwala (2015)
• Solve $\frac{dy}{dx}=\frac{y^2+1}{e^{-x}}$ — BSIC Gujranwala (2015)
• Evaluate $\int ^{\frac{\pi}{4}}_{0}\frac{\sec \theta}{\sin \theta +\cos \theta}d\theta$ — BSIC Gujranwala (2015)
• Evaluate $\int ^{\frac{\pi}{4}}_{0}\cos ^4tdt$ — BSIC Gujranwala (2015), FBSIC(2017)
• Show that $\int \sqrt{a^2-x^2}dx=\frac{a^2}{2}\sin ^{-1}\frac{x}{a}+\frac{x}{2}\sqrt{a^2-x^2}+c$ — BSIC Gujranwala (2015)
• Evaluate $\int \frac{x^3-6x^2+25}{(x+1)^2(x-2)^2}dx$ — FBSIC (2017)
• Evaluate $\int x (\sqrt{x}+1)dx$, (x>0) — FBSIC (2016)
• Evaluate $\int ^{0}_{-2}\frac{1}{(2x-1)^2}dx$— FBSIC (2016)
• Solve the differential equation $(x^2-yx^2)\frac{dy}{dx}+y^2+xy^2=0$. — FBSIC (2016)
• Evaluate $\int \frac{e^{2x}+e^x}{e^x}dx$ — BSIC Rawalpindi(2017)
• Evaluate $\int \cos 3x \sin 2xdx$ — BSIC Rawalpindi(2017)
• Evaluate $\int \frac{x+b}{(x^2+2bx+c)^{\frac{1}{2}}}dx$ — BSIC Rawalpindi(2017)
• Evaluate $\int e^x(\cos x-\sin x)dx$ — BSIC Rawalpindi(2017)
• Evaluate $\int ^{3}_{2}\frac{1}{(x^2+9)^2}dx$ — BSIC Rawalpindi(2017)
• Evaluate $\int ^{\sqrt{5}}_{2}x\sqrt{x^2-1}dx$ — BSIC Rawalpindi(2017)
• What is the linear programming? — BSIC Rawalpindi(2017)
• Solve the differential equation $\frac{1}{x}\frac{dy}{dx}=\frac{1+y^2}{2}$— BSIC Rawalpindi(2017)
• Using differentials to find the value of $^4\sqrt{17}$— BSIC Rawalpindi(2017)
• Evaluate $\int \frac{\sqrt{2}}{\sin x+\cos x}dx$ — BSIC Rawalpindi(2017)
• Evaluate $\int x \sqrt{x^2-1}dx$ — BSIC Sargodha(2016)
• Evaluate $\int (2x+3)^\frac{1}{2}dx$ — BSIC Sargodha(2016)
• Evaluate $\int (\ln x)\frac{1}{x}dx$ — BSIC Sargodha(2016)
• Evaluate $\int \frac{\cot \sqrt{x}}{\sqrt{x}}dx$ — BSIC Sargodha(2016)
• Evaluate $\int \frac{x^2}{4+x^2}dx$ — BSIC Sargodha(2016)
• Evaluate $\int tan^{-1}x dx$ — BSIC Sargodha(2016)
• Evaluate $\int ^{2}_{1}\frac{x}{(x^2+1)}dx$— BSIC Sargodha(2016)
• Find the area between the $x-axis$ and the curve $y=x^2+1$, from $x=1$, to $x=2$— BSIC Sargodha(2016)
• Solve the differential equation $y dx+x dy=0$ — BSIC Sargodha(2016)
• Show that $y=cx-1$, is the solution of the differential equation $x \frac{dy}{dx}=1+y$— BSIC Sargodha(2016)
• Evaluate $\int \frac{7x-1}{(x-1)^2(x+1)}dx$ — BSIC Sargodha(2016)
• Evaluate $\int ^{\frac{\pi}{4}}_{0}\frac{\sin x-1}{(\cos ^2x)}dx$ — BSIC Sargodha(2016)
• Evaluate $\int x \sqrt{x^2-1}dx$ — BSIC Sargodha(2017)
• Evaluate $\int \frac{(\sqrt{\theta}-1)^2}{\sqrt{\theta}}d\theta$ — BSIC Sargodha(2017)
• Evaluate $\int \frac{a}{2\sqrt{at+b}}dt$ — BSIC Sargodha(2017)
• Evaluate $\int \tan^2 xdx$ — BSIC Sargodha(2017)
• Evaluate $\int x \ln xdx$ — BSIC Sargodha(2017)
• Evaluate $\int \frac{3x+1}{x^2-x-6}dx$ — BSIC Sargodha(2017)
• Evaluate $\int ^{\frac{\pi}{4}}_{0}\sec x(\sec x+ \tan x)dx$— BSIC Sargodha(2017)
• Evaluate $\int ^{2}_{-6}\sqrt{3-x}dx$— BSIC Sargodha(2017)
• Solve $\frac{dy}{dx}=\frac{y^2+1}{e^{-x}}$— BSIC Sargodha(2017)
• Evaluate $\int ^{\frac{\pi}{4}}_{0}\frac{1}{1-\sin x}dx$— BSIC Sargodha(2017)
• Evaluate $\int \frac{x \sin^{-1} x}{\sqrt{1-x^2}}dx$ — BSIC Sargodha(2017)
• Solve the differential equation $(y-x\frac{dy}{dx})=2(y^2+\frac{dy}{dx})$— BSIC Sargodha(2017)
• fsc-part2-ptb/important-questions/unit-03-integration