Trigonometry Answers

9 Integrate with respect to x :
∫3−1x7+x2−−−−−√dx
∫−13x7+x2dx

22√
22

42√
42

4−22√
4−22

2√
2
10 Integrate with respect to x :
∫41x+1x√dx
∫14x+1xdx

203
203
20

320
320
-20

5 Evalute
∫x2(3−10x3)dx
∫x2(3−10x3)dx

1150(3−10x3)5)+c
1150(3−10x3)5)+c

110(1−10x2)5)+c
110(1−10x2)5)+c

115(3−20x3)5)+c
115(3−20x3)5)+c

1100(3−2x3)5)+c
1100(3−2x3)5)+c
6 Find the integral with respect to x
∫cosxsinxdx
∫cos⁡xsin⁡xdx

sin2x2+c
sin⁡2x2+c

sin2x+c
sin⁡2x+c

cos2x2+c
cos2⁡x2+c

sinx
sin⁡x

1 Integrate
∫(x3+3x2+2x+4)
∫(x3+3x2+2x+4)

x44+x3+x2+4x+c
x44+x3+x2+4x+c

x42−x3+x2+4x+c
x42−x3+x2+4x+c

3x44+2x3+x+c
3x44+2x3+x+c

6x4−3x2+c
6x4−3x2+c
2 Evaluate
∫(3x−2)6dx
∫(3x−2)6dx

(3x+2)72+c
(3x+2)72+c

(3x+2)721+c
(3x+2)721+c

(3x−2)721+c
(3x−2)721+c

3(3x−2)72+c
3(3x−2)72+c
3 Evaluate
∫cos(6x+4)dx
∫cos⁡(6x+4)dx

sin(6x+4)6+c
sin⁡(6x+4)6+c

cos(6x+4)6+c
cos⁡(6x+4)6+c

tan(6x+4)6+c
tan⁡(6x+4)6+c

sec(6x+4)6+c
sec⁡(6x+4)6+c
4 Evaluate
∫3ex+5cos(x)−10sec2(x)dx
∫3ex+5cos⁡(x)−10sec2⁡(x)dx

3e2+5sinx−10tanx+c
3e2+5sin⁡x−10tan⁡x+c

3ex+cosx−10tanx+c
3ex+cos⁡x−10tan⁡x+c

3ex+5sinx−10secx+c
3ex+5sin⁡x−10sec⁡x+c

2ex−x−10tanx+c

1 Integrate
∫(x3+3x2+2x+4)
∫(x3+3x2+2x+4)

x44+x3+x2+4x+c
x44+x3+x2+4x+c

x42−x3+x2+4x+c
x42−x3+x2+4x+c

3x44+2x3+x+c
3x44+2x3+x+c

6x4−3x2+c
6x4−3x2+c
2 Evaluate
∫(3x−2)6dx
∫(3x−2)6dx

(3x+2)72+c
(3x+2)72+c

(3x+2)721+c
(3x+2)721+c

(3x−2)721+c
(3x−2)721+c

3(3x−2)72+c
3(3x−2)72+c

9 Evaluate
∫x2e3xdx
∫x2e3xdx

e3x3(x2−2x3+29)+c
e3x3(x2−2x3+29)+c

−e3x3(x2+2x3−29)+c
−e3x3(x2+2x3−29)+c

e2x3(x3−x4+29)+c
e2x3(x3−x4+29)+c

ex3(x2+2x3−25)+c
ex3(x2+2x3−25)+c
10 Given f(x) =
(7x4−5x3)
(7x4−5x3)
, evaluate
df(x)dx
df(x)dx

7x4−5x3
7x4−5x3

2x3−15x2
2x3−15x2

28x2−15x2
28x2−15x2

28x3−15x2
28x3−15x2

7 Determine
∫x2+1(x+2)3
∫x2+1(x+2)3

ln(x+2)+4x+2−52(x+3)2+c
ln(x+2)+4x+2−52(x+3)2+c

ln(x+2)−4x+2−52(x+3)2+c
ln(x+2)−4x+2−52(x+3)2+c

−ln(x+2)−4x+2−52(x+3)2+c
−ln(x+2)−4x+2−52(x+3)2+c

ln(x−2)+4x−2−52(x+3)2+c
ln(x−2)+4x−2−52(x+3)2+c
8 Find the volume of a sphere generated by a semicircle
y=(√r2−x2)
y=(r2−x2)
revolving around the x-axis

−π−r32
−π−r32

4πr32
4πr32

πr34
πr34

4πr33
4πr33

5 Find
∫sec3xtanxdx
∫sec3⁡xtan⁡xdx

sin2x+c
sin⁡2x+c

cos2x+c
cos⁡2x+c

sec3x3+c
sec3⁡x3+c

cos3x2+c
cos3⁡x2+c
6 Evaluate
∫x+1x2−3x+2dx
∫x+1x2−3x+2dx

3ln(x+2)−2ln(x+1)+c
3ln(x+2)−2ln(x+1)+c

3ln(x−2)−2ln(x−1)+c
3ln(x−2)−2ln(x−1)+c

−3ln(x−2)−2ln(x−1)+c
−3ln(x−2)−2ln(x−1)+c

3ln(x−2)+2ln(x+1)+c
3ln(x−2)+2ln(x+1)+c

3 Find
∫xcosax2dx
∫xcos⁡ax2dx
with respect to x

cos3x+c
cos3⁡x+c

sin2x+c
sin⁡2x+c

sec2x+1
sec2⁡x+1

12asinax2+c
12asin⁡ax2+c
4 Find the
∫tan3xsec3xdx
∫tan3⁡xsec3⁡xdx

tan2x+1
tan2⁡x+1

cot2x+1
cot2⁡x+1

sec2x+1
sec2⁡x+1

sec2x
sec2⁡x

1 Evaluate
∫e4xdx
∫e4xdx

14e4x+c
14e4x+c

ex+c
ex+c

3ex3+c
3ex3+c

13ex+c
13ex+c
2 Evaluate
∫xe6xdx
∫xe6xdx

x6e6x−1136e6x+c
x6e6x−1136e6x+c

x3e6x+116e6x+c
x3e6x+116e6x+c

x6e6x+1136e6x+c
x6e6x+1136e6x+c

−x6e6x+1136e6x+c
−x6e6x+1136e6x+c

Triangle PQR has a right angle at R. The length of side PR is 9.8 cm, and the length of side QR is 6 cm. Sketch triangle PQR, and find ∠PQR, giving your answer correct to the nearest degree.