Class 12 ISC Maths integration Board Questions
Integration is called the inverse process of differentiation. Instead of differentiating a function, we are given the function’s derivative and asked to find its primitive, i.e., the original function. Such a process is called integration or anti-differentiation. If the function’s derivative is known to us, is it possible to obtain the function. The answer to this question is yes. Integration ( or antiderivative of a function) makes it possible to obtain the original function.
2016
Q1
Evaluate:
∫
tan3x dx
solutions
solutions
Q2
Using properties of definite integrals, evaluate:
∫π/20
solutions
∫π/20
sinx - cos x
/
1+sinx cosx
dx
solutions
Q3
Evaluate:
∫π/20
solutions
∫π/20
sinx + cos x
/
√9 +16 sin2x
dx
solutions
2017
Q1
Evaluate:
∫π/20
(ii) Evaluate:
∫π/40 log(l + tanθ) dθ
solutions
∫π/20
1
/
x2
sin2(
1
/
x
) dx
(ii) Evaluate:
∫π/40 log(l + tanθ) dθ
solutions
Q2
Evaluate:
∫π/20
solutions
∫π/20
sin2x
/
(1+sinx) (2+sinx)
dx
solutions
2018
Q1
Evaluate: ∫ tan-1 √x dx
solutions
solutions
Q2
Evaluate :
∫
solutions
∫
x3 + 5x2 + 4x +1
/
x2
dx
solutions
Q3
(a) Evaluate:
∫
OR
(b) Evaluate:
∫
solutions
∫
x-1
/
√ x2-x
dx
OR
(b) Evaluate:
∫
cos2x
/
1+sinx cosx
dx
solutions
2019
Q1
Evaluate:
∫
OR
Evaluate:
∫3-6 |x+3|dx
solutions
∫
x(1+x2)
/
1+x4
dx
OR
Evaluate:
∫3-6 |x+3|dx
solutions
Q2
Evaluate:
∫ π0
solutions
∫ π0
x tanx
/
secx + tanx
dx
solutions
Q3
Evaluate:
∫
solutions
∫
sec2x
/
cosec2x
dx
solutions
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