বিভিন্ন সূত্রের ব্যবহারে যোগজীকরণ
∫dx25−x2=? \int \frac{d x}{\sqrt{25-x^{2}}} \quad = ? ∫25−x2dx=?
sin−1−x5+c\sin ^{-1} \frac{-x}{5}+\mathrm{c}sin−15−x+c
sin−1x3+c\sin ^{-1} \frac{x}{3}+\mathrm{c}sin−13x+c
sin−1x5+c\sin ^{-1} \frac{x}{5}+\mathrm{c}sin−15x+c
−sin−1x5+c-\sin ^{-1} \frac{x}{5}+\mathrm{c}−sin−15x+c
Solve:
∫dx25−x2=∫dx52−x2=sin−1x5+c \begin{array}{l} \int \frac{d x}{\sqrt{25-x^{2}}} \quad \\ =\int \frac{d x}{\sqrt{5^{2}-x^{2}}}=\sin ^{-1} \frac{x}{5}+\mathrm{c} \end{array} ∫25−x2dx=∫52−x2dx=sin−15x+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?
∫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?
∫x9x4+4dx=? \int \frac{x}{9 x^{4} + 4} dx = ? ∫9x4+4xdx=?
