বিভিন্ন সূত্রের ব্যবহারে যোগজীকরণ
1+x1−x \sqrt{\frac{1 + x}{1 - x}} 1−x1+x
এর ইন্টিগ্রেশন -
sin−1x+1−x2+c \sin^{- 1}{x} + \sqrt{1 - x^{2}} + c sin−1x+1−x2+c
cos−1x−1−x2+c \cos^{- 1}{x} - \sqrt{1 - x^{2}} + c cos−1x−1−x2+c
sin−1x−1−x2+c \sin^{- 1}{x} - \sqrt{1 - x^{2}} + c sin−1x−1−x2+c
cos−1x+1−x2+c \cos^{- 1}{x} + \sqrt{1 - x^{2}} + c cos−1x+1−x2+c
∫1+x1−xdx=∫1+x1−x2dx \int \sqrt{\frac{1+\mathrm{x}}{1-\mathrm{x}}} \mathrm{dx}=\int \frac{1+\mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}} \mathrm{dx} \quad ∫1−x1+xdx=∫1−x21+xdx [হর, লব 1+x \sqrt{1+\mathrm{x}} 1+x দ্বারা গুণ] =∫dx1−x2−12∫−2x1−x2dx=sin−1x−1−x2+c =\int \frac{d x}{\sqrt{1-x^{2}}}-\frac{1}{2} \int \frac{-2 x}{\sqrt{1-x^{2}}} d x=\sin ^{-1} x-\sqrt{1-x^{2}}+c =∫1−x2dx−21∫1−x2−2xdx=sin−1x−1−x2+c
∫sin(5−x10)dx=f(x)+c \int \sin{\left ( 5 - \frac{x}{10} \right )} dx = f{\left ( x \right )} + c ∫sin(5−10x)dx=f(x)+c হলে, f(x)এর মান কত?
∫dx25−x2=? \int \frac{d x}{\sqrt{25-x^{2}}} \quad = ? ∫25−x2dx=?
∫dx1−x2=?\int \frac{d x}{1-x^{2}} = ?∫1−x2dx=?
g(x)=x g(x)=\sqrt{x} g(x)=x হলে-
i. ∫1g(x)dx=2x+c \int \frac{1}{g(x)} d x=2 \sqrt{x}+c ∫g(x)1dx=2x+c
ii. ∫01g(x)dx=23 \int_{0}^{1} g(x) d x=\frac{2}{3} ∫01g(x)dx=32
iii. ∫sec2xdxg(tanx)=2tanx+c \int \frac{\sec ^{2} x d x}{g(\tan x)}=2 \sqrt{\tan x}+c ∫g(tanx)sec2xdx=2tanx+c
নিচের কোনটি সঠিক?
