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201-NYA-05, Exams of Calculus

University of HuddersfieldCalculus

201-NYA-05 - Calculus 1. WORKSHEET: INTEGRALS. Evaluate the following indefinite integrals: 1. ∫. (4x + 3) dx. 2. ∫. (4x2 - 8x + 1) dx.

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2021/2022

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201-NYA-05 - Calculus 1
WORKSHEET: INTEGRALS
Evaluate the following indefinite integrals:
1. Z(4x+ 3) dx
2. Z(4x2−8x+ 1) dx
3. Z(9t2−4t+ 3) dt
4. Z(2t3−t2+ 3t−7) dt
5. Z1
z3−3
z2dz
6. Z4
z7−7
z4+zdz
7. Z3√u+1
√udu
8. Z(√u3−1
2u−2+ 5) du
9. Z(2v5/4+ 6v1/4+ 3v−4)dv
10. Z(3v5−v5/3)dv
11. Z(3x−1)2dx
12. Zx−1
x2
dx
13. Zx(2x+ 3) dx
14. Z(2x−5)(3x+ 1) dx
15. Z8x−5
3
√xdx
16. Z2x2−x+ 3
√xdx
17. Zx3−1
x−1dx
18. Zx3+ 3x2−9x−2
x−2dx
19. Z(t2+ 3)2
t6dt
20. Z(√t+ 2)2
t3dt
21. Z3
4cos u du
22. Z−1
5sin u du
23. Z7
csc xdx
24. Z1
4 sec xdx
25. Z(√t+ cos t)dt
26. Z(3
√t2−sin t)dt
27. Zsec t
cos tdt
28. Z1
sin2tdt
29. Z(csc vcot vsec v)dv
30. Z(4 + 4 tan2v)dv
31. Zsec wsin w
cos wdw
32. Zcsc wcos w
sin wdw
33. Z(1 + cot2z) cot z
csc zdz
34. Ztan z
cos zdz
35. Zd
dx px2+ 4 dx
36. Zd
dx
3
px3−8dx
37. Zd
dx sin 3
√x dx
38. Zd
dx √tan x dx
39. d
dx Zx3√x−4dx
40. d
dx Zx43
px2+ 9 dx
41. d
dx Zcot x3dx
42. d
dx Zcos px2+ 1 dx
pf3

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201-NYA-05 - Calculus 1

WORKSHEET: INTEGRALS

Evaluate the following indefinite integrals:

(4x + 3) dx

(4x^2 − 8 x + 1) dx

(9t^2 − 4 t + 3) dt

(2t^3 − t^2 + 3t − 7) dt

∫ (^

z^3 −^

z^2

dz

∫ (^4

z^7

z^4

  • z

dz

u +

√^1

u

du

u^3 − 1 2

u−^2 + 5) du

(2v^5 /^4 + 6v^1 /^4 + 3v−^4 ) dv

(3v^5 − v^5 /^3 ) dv

(3x − 1)^2 dx

x − 1 x

dx

x(2x + 3) dx

(2x − 5)(3x + 1) dx

8 x − 5 √ (^3) x dx

2 x^2 − √ x + 3 x dx

x^3 − 1 x − 1

dx

x^3 + 3x^2 − 9 x − 2 x − 2

dx

(t^2 + 3)^2 t^6 dt

t + 2)^2 t^3

dt

cos u du

sin u du

csc x

dx

4 sec x

dx

t + cos t) dt

t^2 − sin t) dt

sec t cos t

dt

sin^2 t

dt

(csc v cot v sec v) dv

(4 + 4 tan^2 v) dv

sec w sin w cos w dw

csc w cos w sin w

dw

(1 + cot^2 z) cot z csc z dz

tan z cos z

dz

d dx

x^2 + 4 dx

∫ (^) d

dx

√ (^3) x (^3) − 8 dx

∫ (^) d

dx

sin 3

x dx

d dx

tan x dx

d dx

x^3

x − 4 dx

d dx

x^4

x^2 + 9 dx

d dx

cot x^3 dx

d dx

cos

x^2 + 1 dx

Solve the differential equation subject to the given conditions:

  1. f ′(x) = 12x^2 − 6 x + 1 f (1) = 5

  2. f ′(x) = 9x^2 + x − 8 f (−1) = 1

dy dx

= 4x^1 /^2 y = 21 when x = 4

Evaluate the following definite integrals:

0

2 x dx

2

3 dv

− 1

(x − 2) dx

2

(− 3 v + 4) dv

− 1

(t^2 − 2) dt

0

(3x^2 + x − 2) dx

0

(2t − 1)^2 dt

− 1

(t^3 − 9 t) dt

1

x^2

dx

− 2

u −

u^2

du

1

u − 2 √ u

du

− 3

v^1 /^3 dv

− 1

t − 2) dt

1

x dx

0

x −

x 3

dx

0

(2 − t)

t dt

− 1

(t^1 /^3 − t^2 /^3 ) dt

− 8

x − x^2 2 3

x dx

0

| 2 x − 3 | dx

0

|x^2 − 4 x + 3| dx

∫ (^) π

0

(1 + sin x) dx

∫ (^) π/ 4

0

1 − sin^2 θ cos^2 θ

dθ

∫ (^) π/ 6

−π/ 6

sec^2 x dx

∫ (^) π/ 2

π/ 4

(2 − csc^2 x) dx

∫ (^) π/ 3

−π/ 3

4 sec θ tan θ dθ

∫ (^) π/ 2

−π/ 2

(2t + cos t) dt

∫ (^) e

1

2 x +^1 x

dx

1

x + 1 x

dx

0

(ex^ + 6) dx

0

(t − et) dt

− 1

(eθ^ + sin θ) dθ

∫ (^2) e

e

cos x − 1 x

dx