In this article, we share MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 Pdf, These solutions are solved by subject experts from the latest MP Board books.

MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1

निम्नलिखित फलनों के प्रतिअवकलज (समाकलन) निरीक्षण विधि द्वारा ज्ञात कीजिए। –
प्रश्न 1.
sin2x
हल:
हम जानते हैं कि \(\frac{d}{d x}\) cos 2x = – 2 sin 2x
या sin 2x = \(-\frac{1}{2} \frac{d}{d x}\)cos2x
sin 2x = \(\frac{d}{d x}\)(\(-\frac{1}{2}\)cos2x)
अतः sin 2x का प्रति अवकलज \(-\frac{1}{2}\)cos 2x है।

प्रश्न 2.
cos 3x
हल:
हम जानते हैं कि \(\frac{d}{d x}\) sin 3x = 3 cos3x
या cos3x = \(\frac{d}{d x}\)(\(\frac{1}{3}\) sin 3x)
अत: cos3x का प्रति अवकलज \(\frac{1}{3}\) sin 3x हैं।

प्रश्न 3.
e2x
हल:
हम जानते हैं कि \(\frac{d}{d x}\)e2x = 2e2x
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 1

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प्रश्न 4.
(ax + b)2
हल:
हम जानते हैं कि
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 2

प्रश्न 5.
sin 2x – 4e3x
हल:
हम जानते हैं
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 3

निम्नलिखित समाकलनों को ज्ञात कीजिए।
प्रश्न 6.
\(\int\left(4 e^{3 x}+1\right)\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 4

प्रश्न 7.
\(\int x^{2}\left(1-\frac{1}{x^{2}}\right)\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 5

MP Board Solutions

प्रश्न 8.
\(\int\left(a x^{2}+b x+c\right) d x)\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 6

प्रश्न 9.
\(\int\left(2 x^{2}+e^{x}\right) d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 7

प्रश्न 10.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 8
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 9

प्रश्न 11.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 33
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 10

MP Board Solutions

प्रश्न 12.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 11
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 12

प्रश्न 13.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 13
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 14

प्रश्न 14.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 15
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 16

प्रश्न 15.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 17
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 18

MP Board Solutions

प्रश्न 16.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 19
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 20

प्रश्न 17.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 21
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 22

प्रश्न 18.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 23
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 24

प्रश्न 19.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 25
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 26

प्रश्न 20.
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 27
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 28

MP Board Solutions

प्रश्न 21 एवं 22 में सही उत्तर का चयन कीजिए-
प्रश्न 21.
\(\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)\) का प्रतिअबकलज है-
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 29
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 34
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 30
अतः विकल्प (C) सही है।

प्रश्न 22.
यदि \(\frac{d}{d x}\) f(x) = 4x3 – \(\frac{3}{x^{4}}\) जिसमें f(2) = 0 तो f(x) है-
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 31
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.1 img 32
अत: विकल्प (A) सही है।