PRACTICE PROBLEMS USING INTEGRATION

Question 1 :

(i)  ∫cosec (2-x) cot (2-x) dx

(ii)  ∫cosec (4x+2) cot (4x+2) dx

(iii)  ∫cosec (3-2x) cot (3-2x) dx

(iv)  ∫cosec (Lx+m) cot (Lx+m) dx

Solution

Question 2 :

(i)  ∫ sec (3+x) tan (3+x) dx

(ii)  ∫ sec (3x+4) tan (3x+4) dx

(iii)  ∫ sec (4-x) tan (4-x) dx

(iv)  ∫ sec (4-3x) tan (4-3x) dx

(v)  sec (ax+b) tan (ax+b) dx

Solution

Question 3 :

(i)  ∫cosec (2-x) cot (2-x) dx

(ii)  ∫cosec (4x+2) cot (4x+2) dx

(iii)  ∫cosec (3-2x) cot (3-2x) dx  

(iv)  ∫cosec (Lx+m) cot (Lx+m) dx

Solution

Question 4 :

(i)  1/cos² (px + a)

(ii)  1/sin² (L - m x)

Solution

(1)  5x4+3(2x+3)4-6(4-3x)5

(2)  (3/x)+[m/(4x+1)]-2(5-2x)5

(3)  4 - 5/(x+2) + 3 cos 2x

(4)  3e7x-4sec(4x+3)tan(4x+3)+11/x5

(5)  pcosec2(px-q)-6(1-x)4+4e(3-4x)

(6)  (2x-5) (36+4x)

(7)  (1 + x3)2

(8)  (x3+4x2-3x+2)/x2

(9)  (x4 - x2 + 2)/(x + 1)

(10)  (1+x)2/√x

Solution

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