In this article, we share MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 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 7.9

1 से 20 तक के प्रश्नों में निश्चित समाकलनों का मान ज्ञात कीजिए-
प्रश्न 1.
\(\int_{-1}^{1}(x+1)\) dx
हल:
समाकलन करने पर
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 1

प्रश्न 2.
\(\int_{2}^{3} \frac{1}{x}\) dx
हल:
माना I = \(\int_{2}^{3} \frac{1}{x}\) dx
= \([\log x]_{2}^{3}\) = log 3 – log 2 = log\(\frac{3}{2}\)

प्रश्न 3.
\(\int_{1}^{2}\left(4 x^{3}-5 x^{2}+6 x+9\right)\) dx
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 2

प्रश्न 4.
\(\int_{0}^{\pi / 4} \sin 2 x\) dx
हल:
माना I = \(\int_{0}^{\pi / 4} \sin 2 x\) dx
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 3

MP Board Solutions

प्रश्न 5.
\(\int_{0}^{\pi / 2} \cos 2 x\) dx
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 4

प्रश्न 6.
\(\int_{4}^{5} e^{x} d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 5

प्रश्न 7.
\(\int_{0}^{\pi / 4} \tan x d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 6

प्रश्न 8.
\(\int_{\pi / 6}^{\pi / 4} \csc x d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 7

MP Board Solutions

प्रश्न 9.
\(\int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}}\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 8

प्रश्न 10.
\(\int_{0}^{1} \frac{d x}{1+x^{2}}\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 9

प्रश्न 11.
\(\int_{2}^{3} \frac{d x}{x^{2}-1}\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 10

प्रश्न 12.
\(\int_{0}^{\pi / 2} \cos ^{2} x d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 11
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 12

MP Board Solutions

प्रश्न 13.
\(\int_{2}^{3} \frac{x d x}{x^{2}+1}\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 13

प्रश्न 14.
\(\int_{0}^{1} \frac{2 x+3}{5 x^{2}+1} d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 14

प्रश्न 15.
\(\int_{0}^{1} x e^{x^{2}} d x\)
हल:
x2 = t प्रतिस्थापित करने पर
x dx = \(\frac{1}{2}\) dt
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 15

प्रश्न 16.
\(\int_{1}^{2} \frac{5 x^{2}}{x^{2}+4 x+3}\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 16
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 17
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 18

MP Board Solutions

प्रश्न 17.
\(\int_{0}^{\pi / 4}\left(2 \sec ^{2} x+x^{3}+2\right) d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 19

प्रश्न 18.
\(\int_{0}^{\pi}\left(\sin ^{2} \frac{x}{2}-\cos ^{2} \frac{x}{2}\right) d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 20

प्रश्न 19.
\(\int_{0}^{2} \frac{6 x+3}{x^{2}+4} d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 21
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 22

प्रश्न 20.
\(\int_{0}^{1}\left(x e^{x}+\sin \frac{\pi x}{4}\right) d x\)
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 23

MP Board Solutions

प्रश्न 21 एवं 22 में सही उत्तर का चयन कीजिए-
प्रश्न 21.
\(\int_{1}^{\sqrt{3}} \frac{d x}{1+x^{2}}\) बराबर है-
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 24
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 25
अतः विकल्प (D) सही है।

प्रश्न 22.
\(\int_{0}^{2 / 3} \frac{d x}{4+9 x^{2}}\) बराबर है-
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 26
हल:
MP Board Class 12th Maths Book Solutions Chapter 7 समाकलन Ex 7.9 27
अतः विकल्प (D) सही है।

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