Question

Who can here provide me a lot questions of derivation and integration of class 11 chse ?​

Answer 1

Integrate 1/(1+x2) for limit [0,1].

Solution:

I=∫1011+x2dx

=[tan−1x]10

=[tan−11−tan−10]

=[π4−0]

=π4

∫1011+x2dx=π4

2] Find the value of ∫2x cos (x2 – 5).

Solution: Let, I = ∫2xcos(x2 – 5).dx

Let x2 – 5 = t …..(1)

2x.dx = dt

Substituting these values, we have

I = ∫cos(t).dt

= sin t + c …..(2)

Substituting the value of 1 in 2, we have

= sin (x2 – 5) + C

3] What is the value of ∫ 8 x3 dx.

Solution:

∫ 8 x3 dx = 8 ∫ x3 dx

= 8 x4 / 4 + C

= 2 x4 + C

4] Find the value of ∫ Cos x + x dx.

Solution: ∫ Cos x + x dx = ∫ Cos x dx + ∫ x dx

= sin x + x2/2 + C

5] Solution: I = ∫(xe+ex+ee) dx

Let us split the above equation.

∫xe dx + ∫ex dx + ∫ee dx

By the formula, we know;

∫xn dx = xn+1/n+1

Therefore,

xe+1/e+1 + ∫ex dx + ∫ee dx

By formula, ∫axdx = ax/log a, we can write the above equation as:

xe+1/e+1 + ex/logee + ∫ee dx

By formula, ∫kdx = kx+c, we can write the above equation as:

xe+1/e+1 + ex/logee + ee x + c

practice questions:

b

Integrate ∫ e-x dx for [0,∞].

Integrate ∫x/(x+1) dx for [0,1]

Find ∫(ax2+bx+c) dx

Find ∫(2x2+ex) dx

Find ∫[(x3+3x+4)/√x] dx

Evaluate ∫[(1-x)√x] dx

Evaluate ∫sec x(sec x+tan x) dx

Find the integration of 2x/1+x2

Find the integration of sin x cox(sin x)

What is the value of ∫[sin (ax+b) cos(ax+b)] dx.