Erik Lehnsherr
New member
- Joined
- Jun 13, 2010
- Messages
- 11
Are these correct? Did I miss anything?
1.Prove that ∫02x2(x2+4)dx=62−ln(3+22)
u=x2+4u−4=x2
\(\displaystyle = \int \frac{(u - 4)u^\frac{1}{2}}{2(u - 4)^\frac{1}{2}}\,\dot\,du\,\,\,\,\,\,\,\,\,du = 2x\,dx\)
dxdu=dx
\(\displaystyle = \frac{1}{2}\int\frac{ (u - 4)^1}{u - 4^\frac{1}{2}}\,\dot\,\,u^\frac{1}{2}\)
=21∫(u−4)u23−4u21
2.Show that∫710x2−5x−67dx=ln(1132)
∫710x2−5x−67dx=(x−6)A+(x+1)B
Ax+A+Bx−6B
A+B=0,A−6b=7
A=−B(−B)−6B=7
∴A=1−7B=7B=−1
(x−6)1+x+11
[ln∣x−6∣−ln∣x+1∣]710+C
ln∣x+1x−6∣−ln∣x+1x−6∣
ln∣114∣−ln∣81∣
ln(81114)
ln(114×8)=ln(1132)
1.Prove that ∫02x2(x2+4)dx=62−ln(3+22)
u=x2+4u−4=x2
\(\displaystyle = \int \frac{(u - 4)u^\frac{1}{2}}{2(u - 4)^\frac{1}{2}}\,\dot\,du\,\,\,\,\,\,\,\,\,du = 2x\,dx\)
dxdu=dx
\(\displaystyle = \frac{1}{2}\int\frac{ (u - 4)^1}{u - 4^\frac{1}{2}}\,\dot\,\,u^\frac{1}{2}\)
=21∫(u−4)u23−4u21
2.Show that∫710x2−5x−67dx=ln(1132)
∫710x2−5x−67dx=(x−6)A+(x+1)B
Ax+A+Bx−6B
A+B=0,A−6b=7
A=−B(−B)−6B=7
∴A=1−7B=7B=−1
(x−6)1+x+11
[ln∣x−6∣−ln∣x+1∣]710+C
ln∣x+1x−6∣−ln∣x+1x−6∣
ln∣114∣−ln∣81∣
ln(81114)
ln(114×8)=ln(1132)