7 समाकलन | प्रश्नावली 7.1 | NCERT Maths Class 12 Chapter 7 Exercise 7.1 all questions UP Board Hindi Medium
7 समाकलन | प्रश्नावली 7.1 | NCERT Maths Class 12 Chapter 7 Exercise 7.1 all questions UP Board Hindi Medium 7 समाकलन (Integrals) प्रश्नावली (7.1) NCERT Math Class 12th SOLVED By : AJAY SIR (1/9/2025) 1. $sin2x$ हल :- $∫sin2x dx= ?$ $d/{dx} cos2x = - sin2x .2$ ${-1}/2 d/{dx} cos2x = sin2x$ $d/{dx} ({-1}/2 cos2x )= sin2x$ $∫sin2x dx={-1}/2 cos2x$ Ans. 2. $cos3x$ हल :- $∫cosx dx= ?$ $d/{dx} sin3x = cos3x .3$ $1/3 d/{dx} sin3x = cos3x$ $d/{dx} (1/3 sin3x)= cos3x$ $∫cos3x dx=1/3 sin3x $ Ans. 3. $e^{2x}$ हल :- $∫e^{2x} dx= ?$ $d/{dx} e^{2x}= e^{2x}.2$ $1/2 d/{dx} e^{2x}=e^{2x}$ $d/{dx} ({1/2} e^{2x})=e^{2x}$ $∫e^{2x} dx=1/2 e^{2x}$ Ans. 4. ${(ax+b)}^2$ हल :- $∫{(ax+b)}^2 dx= ?$ $d/{dx} {(ax+b)}^3= {(ax+b)}^2 . d/{dx} (ax+b)$ $d/{dx} {(ax+b)}^3= 3{(ax+b)}^2 .a$ $1/{3a} d/{dx} {(ax+b)}^3={(ax+b)}^2$ $d/{dx} [1/{3a} {(ax+b)}^3]= cos3x$ $∫{(ax+b)}^2 dx=1/{3a} {(ax+b)}^3$ Ans. 5. $sin2x-4e^{3x}$ हल :- $∫(sin2x-4e^{3x}) dx= ...