7 समाकलन | प्रश्नावली 7.1 | NCERT Maths Class 12 Chapter 7 Exercise 7.1 all questions UP Board Hindi Medium

सितंबर 02, 2025

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 :-

$∫(sin2x-4e^{3x}) dx= ?$
∵ $∫(sin2x-4e^{3x}) dx= ∫sin2x dx- 4∫e^{3x} dx$
$⇒ d/{dx} cos2x = - sin2x .2$
${-1}/2 d/{dx} cos2x = sin2x$
$d/{dx} ({-1}/2 cos2x )= sin2x$
$∫sin2x dx={-1}/2 cos2x (1)$
$⇒d/{dx} e^{3x} = e^{3x}.3$
$1/2 d/{dx} e^{3x}=e^{3x}$
$d/{dx} (1/3 e^{3x})=e^{3x}$
$∫e^{3x} dx=1/3 e^{3x}$ Ans.
∴ $∫(sin2x-4e^{3x}) dx=-1/2 cos2x - 4× 1/3 e^{3x}$
$∫(sin2x-4e^{3x}) dx={-1}/2 cos2x- 4/3 e^{3x}$ Ans.

6. $sin2x-4e^{3x}$

हल :-