Find the area of the region bounded by the parabola y = x 2 + 1 and the lines y = x, x = 0 and x = 2. - Wired Faculty

Vector Algebra

Question

Find the area of the region bounded by the parabola y = x² + 1 and the lines y = x, x = 0 and x = 2.

Solution

We are to find the area of the region bounded by the curves.
   $straight y space equals space straight x squared plus 1 comma straight y space equals space straight x comma straight x space equals space 0$
and x = 2
Now    $straight y space equals space straight x squared plus 1$ is an upward parabola with vertex A (0, 1), y =x is straight line passing through the origin, B(2, 2) and lies below the parabola.
Now area bounded by the parabola, above the x-axis and ordinates x = 0, x = 2.
   $equals space integral subscript 0 superscript 2 left parenthesis straight x squared plus 1 right parenthesis space dx space equals space open square brackets straight x cubed over 3 plus straight x close square brackets subscript 0 superscript 2 space equals space open parentheses 8 over 3 plus 2 close parentheses space minus space left parenthesis 0 plus 0 right parenthesis space equals space 14 over 3$
Area bounded by the line y = x, above the x-axis and ordinates x = 0, x = 2.
   $equals space integral subscript 0 superscript 2 straight x space dx space equals space open square brackets straight x squared over 2 close square brackets subscript 0 superscript 2 space equals space 4 over 2 minus 0 space equals space 2$
   $therefore space required space area space equals space 14 over 3 minus 2 space equals space 8 over 3 space sq. space units.$

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Vector Algebra

Find the area of the region bounded by the parabola y = x² + 1 and the lines y = x, x = 0 and x = 2.

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Vector Algebra

Find the area of the region bounded by the parabola y = x2 + 1 and the lines y = x, x = 0 and x = 2.

Some More Questions From Vector Algebra Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the area of the region bounded by the parabola y = x² + 1 and the lines y = x, x = 0 and x = 2.