These NCERT Solutions for Class 12 Maths Chapter 7 समाकलन Ex 7.8 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 12 Maths Chapter 7 समाकलन Ex 7.8
प्रश्न 1.
\(\int_a^b\)x dx
हल:
प्रश्न 2.
\(\int_0^5\) (x + 1) dx
हल:
प्रश्न 3.
\(\int_3^2\) (x2 ) dx
हल:
प्रश्न 4.
\(\int_4^1\) (x2 – x ) dx
हल:
माना
\(\int_b^a\) f(x) dx = \(\int_4^1\) (x2 – x ) dx
यहाँ f(x) = x2 – x, a = 1, b = 4
(b – a) = (4 – 1) = -3
∴ nh = 3
f(a) = f(1) = 12 – 1 = 0
f(a + h) = f(1 + h)
= (1 + h)2 – (1 + h)
= 1 + 2h + h2 – 1 – h = h2 + h
f(a + 2h) = f(1 + 2h)
= (1 + 2h)2 – (1 + 2h)
= 1 + 2.2h + 4h2 – 1 – 2h = 4h2 + 2h
f(a + 3h) = f(1 + 3h)
= (1 + 3h)2 – (1 + 3h)
= 1 + 2.3h + 9h2 – 1 – 3h = 9h2 + 3h
f[a + (n – 1)h]
= f[1 + (n – 1)h]
= [1 + (n – 1)h]2 – 1[1 + (n – 1)h]
= 1 + 2(n – 1)h + (n – 1)2h2 – 1 – (n – 1)h
= (n – 1)2h2 + (n – 1)h
प्रश्न 5.
\(\int_1^1\) ex dx
हल:
प्रश्न 6.
\(\int_1^1\) ex dx
हल:
