P1^
6
Exercise(^) 6B
EXERCISE 6B 1 Find the following indefinite integrals.
(i) (^) ∫ 3 x^2 dx (ii) (^) ∫(5x^4 + 7 x^6 ) dx
(iii) (^) ∫(6x^2 + 5) dx (iv) (^) ∫(x^3 + x^2 + x + 1) dx
(v) (^) ∫(11x^10 + 10 x^9 ) dx (vi) (^) ∫(3x^2 + 2 x + 1) dx
(vii) (^) ∫(x^2 + 5) dx (viii) (^) ∫ 5 dx
(ix) (^) ∫(6x^2 + 4 x) dx (x) (^) ∫(x^4 + 3 x^2 + 2 x + 1) dx
2 Find the following indefinite integrals.
(i) (^) ∫ 10 x–4 dx (ii) (^) ∫(2x − 3 x–4) dx
(iii) (^) ∫(2 + x^3 + 5 x–3) dx (iv) (^) ∫(6x^2 − 7 x–2 ) dx
(v) (^) ∫ 5
(^14)
∫ xxd^ (vi)^ ∫^14
x
∫ dx
(vii) (^) ∫∫ xxd (viii) (^) ∫ 2 x^442
x
∫()− dx^
3 Evaluate the following definite integrals.
(i) (^) ∫ 122 x dx (ii) (^) ∫^302 x dx
(iii) (^) ∫
3
03 x
(^2) dx (iv) (^) ∫^5
1 x dx^
(v) (^) ∫ 56 (2x^ + 1) dx (vi) (^) ∫−^21 (2x +^ 4) dx
(vii) (^) ∫
5
3 (3x
(^2) + (^2) x) dx (viii)
∫
1
0 x
(^5) dx
(ix) (^) ∫
− 1
− 2 (x
(^4) + (^) x (^3) ) dx (x)
∫
1
− 1 x
(^3) dx
(xi) (^) ∫
4
− 5 (x
(^3) + (^3) x ) dx (xii)
∫
− 2
− 35 dx
4 Evaluate the following definite integrals.
(i) (^) ∫^413 x–2 dx (ii) (^) ∫^428 x–3 dx
(iii) (^) ∫^4112
(^12)
∫ xxd^ (iv)^ ∫–1–3^63
x
∫ dx^
(v) (^) ∫^2 0.5 xx
x
x
2
4
++ 34
∫ d
(vi) (^) ∫^94 x
x
− x
∫
(^1) d