Exercise 3.3
Exercise 3.3
Exercise 3.3
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MA111: Prepared by Dr.Archara Pacheenburawana 45<br />
Answer to <strong>Exercise</strong> 5.3<br />
1. (a) 2π (b) π(1−1/e) (c) 64π/15 2. (a) 21π/2 (b) 1944π/5 (c) 5π/6<br />
3. (a) 36√ 3<br />
5<br />
π (b) 40√ 5<br />
3<br />
π (c) 23π<br />
30<br />
(d) π 2<br />
(e) 8π 3<br />
Find the length of the curve.<br />
<strong>Exercise</strong> 5.4<br />
1. y = 1 3 (x2 +2) 3/2 , 0 ≤ x ≤ 1<br />
2. y = x4<br />
4 + 1<br />
8x 2, 1 ≤ x ≤ 3<br />
3. y = ln(secx), 0 ≤ x ≤ π/4<br />
4. y = ln(1−x 2 ), 0 ≤ x ≤ 1 2<br />
5. y = coshx, 0 ≤ x ≤ 1<br />
Answer to <strong>Exercise</strong> 5.4<br />
1.<br />
4<br />
3<br />
2. 181<br />
9<br />
3. ln( √ 2+1) 4. ln3− 1 2<br />
5. sinh1<br />
<strong>Exercise</strong> 6.1<br />
Evaluate the integral.<br />
∫<br />
∫<br />
1. xe 2x dx 2. x 2 lnxdx<br />
∫<br />
∫<br />
3. xsin4xdx 4. x 2 e −3x dx<br />
∫<br />
∫<br />
5. x 2 cos3xdx 6. e x sin4xdx<br />
∫<br />
∫<br />
7. (lnx) 2 dx 8. cosxcos2xdx<br />
∫<br />
∫<br />
9. xsec 2 xdx 10. cosxln(sinx)dx<br />
∫<br />
∫<br />
11. cos(lnx)dx 12. cos −1 xdx<br />
∫<br />
13. sin √ ∫ 1<br />
xdx 14. xsin2xdx<br />
15.<br />
17.<br />
∫ 1<br />
0<br />
∫ 4<br />
1<br />
xe −x dx 16.<br />
ln √ xdx 18.<br />
0<br />
∫ 2<br />
1<br />
∫ 2<br />
1<br />
lnx<br />
x 2 dx<br />
x 4 (lnx) 2 dx
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