find the volume of a solid generated by revolving the region counted by y=x²-4x+3 about x axis?
Answers
Answer:
Volume
Volume=∫πy^2 dx for x=1 to 4
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4= π(4^5/5 -2*4^4+26*4^3/3-20*4^2+25*4)
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4= π(4^5/5 -2*4^4+26*4^3/3-20*4^2+25*4)- π(1^5/5 -2*1^4+26*1/3-20*1^2+25*1)
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4= π(4^5/5 -2*4^4+26*4^3/3-20*4^2+25*4)- π(1^5/5 -2*1^4+26*1/3-20*1^2+25*1)= π(1024/5 -512+26*64/3-320+100)
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4= π(4^5/5 -2*4^4+26*4^3/3-20*4^2+25*4)- π(1^5/5 -2*1^4+26*1/3-20*1^2+25*1)= π(1024/5 -512+26*64/3-320+100)- π(1/5 -2+26/3-20+25)
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4= π(4^5/5 -2*4^4+26*4^3/3-20*4^2+25*4)- π(1^5/5 -2*1^4+26*1/3-20*1^2+25*1)= π(1024/5 -512+26*64/3-320+100)- π(1/5 -2+26/3-20+25)= π(1023/5 -510+546-300+75)
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4= π(4^5/5 -2*4^4+26*4^3/3-20*4^2+25*4)- π(1^5/5 -2*1^4+26*1/3-20*1^2+25*1)= π(1024/5 -512+26*64/3-320+100)- π(1/5 -2+26/3-20+25)= π(1023/5 -510+546-300+75)= π(1023/5 -189)
Volume=∫πy^2 dx for x=1 to 4=∫π(x^2-4x+5)^2 dx for x=1 to 4=∫π(x^4+16x^2+25-8x^3-40x+10x^2) dx for x=1 to 4= π(x^5/5 +16x^3/3+25x-8x^4/4-40x^2/2+10x^3/3) for x=1 to 4= π(x^5/5 -2x^4+26x^3/3-20x^2+25x) for x=1 to 4= π(4^5/5 -2*4^4+26*4^3/3-20*4^2+25*4)- π(1^5/5 -2*1^4+26*1/3-20*1^2+25*1)= π(1024/5 -512+26*64/3-320+100)- π(1/5 -2+26/3-20+25)= π(1023/5 -510+546-300+75)= π(1023/5 -189)= 15.6π