intigration of Rational Algebraic Fractions (মূলদ ভগ্নাংশ)
দৃশ্যকল্প: g(x)=cot−1x,f(x)=x g(x)=\cot ^{-1}x, f(x)=x g(x)=cot−1x,f(x)=x
P=(x−4)2(x−3) P=(x-4)^{2}(x-3) P=(x−4)2(x−3)
∫dx1−4x2 \int \frac{\mathrm{dx}}{\sqrt{1-4 \mathrm{x}^{2}}}∫1−4x2dx নির্ণয় কর।
∫13f(x)g(x)dx \int_{1}^{\sqrt{3}} f(x) g(x) d x ∫13f(x)g(x)dx নির্ণয় কর
∫f(x)Pdx \int \frac{f(x)}{P} d x ∫Pf(x)dx নির্ণয় কর।
f(x)=x2 f(x)=x^{2} f(x)=x2 এবং x2a2+y2b2=1 \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 a2x2+b2y2=1
দৃশ্যকল্প-১: f(x)=x+3(x−1)(x2+5)f(x)=\frac{x+3}{(x-1)\left(x^{2}+5\right)}f(x)=(x−1)(x2+5)x+3.
দৃশ্যকল্প-২: y2=8x,x−y=0\mathrm{y}^{2}=8 \mathrm{x}, \mathrm{x}-\mathrm{y}=0y2=8x,x−y=0.
দৃশ্যকল্প-১: f(x)=x+6 f(x)=x+6 f(x)=x+6
দৃশ্যকল্প-২: g(x)=x2 \mathrm{g}(\mathrm{x})=\mathrm{x}^{2} g(x)=x2
x2+y2=36…(i)f(y)=y−1,g(y)=y2+4…(ii) \begin{array}{l}x^{2}+y^{2}=36…(i) \\ f(y)=y-1, g(y)=y^{2}+4…(ii) \end{array} x2+y2=36…(i)f(y)=y−1,g(y)=y2+4…(ii)
