-->

Vector Algebra

Question
CBSEENMA12032688

Find the area under the given curves and given lines:
(i) y = x2, x = 1, x = 2 and x-axis
(ii) y - x4, x = 1, x = 5 and x -axis

Solution

(i) The given curve and lines are
y = x2, x = 1, x = 2 and x-axis
Required area = integral subscript 1 superscript 2 straight y space dx space equals space integral subscript 1 superscript 2 straight x squared dx space equals space open square brackets straight x cubed over 3 close square brackets subscript 1 superscript 2 space equals space 8 over 3 minus 1 third space equals space 7 over 3
(ii) The given curve and lines are
 y = x4, x = 1, x = 5 and x-axis
Required area  = integral subscript 1 superscript 5 straight y space dx space space equals space integral subscript 1 superscript 5 straight x to the power of 4 dx space space equals open square brackets straight x to the power of 5 over 5 close square brackets subscript 1 superscript 5 space equals space fraction numerator left parenthesis 5 right parenthesis to the power of 5 over denominator 5 end fraction minus fraction numerator left parenthesis 1 right parenthesis to the power of 5 over denominator 5 end fraction
space space space space space space space space space space space space space space space space space equals 3125 over 5 minus 1 fifth space equals space 3124 over 5 space sq. space units.

Some More Questions From Vector Algebra Chapter