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Vector Algebra

Question
CBSEENMA12032684
Wired Faculty App

Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis in the first quadrant.

Solution

The equation of curve is y2 = x
Required area = integral subscript 1 superscript 4 space straight y space dx space equals space integral subscript 1 superscript 4 square root of straight x space end root dx space equals integral subscript 1 superscript 4 straight x to the power of 1 half end exponent dx
                        WiredFaculty

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Question
CBSEENMA12032685
Wired Faculty App

Find the area of the region bounded by y2 = 4 x, x = 1, x = 4 and the x-axis in the first quadrant.   

Solution

The equation of curve is y2 = 4 x
Required area  = WiredFacultyintegral subscript 1 superscript 4 straight y space dx
            WiredFaculty
WiredFaculty

Question
CBSEENMA12032686
Wired Faculty App

Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.

Solution

The equation of curve is y2 = 9x, which is right handed parabola.
Two lines are x = 2,  x = 4.
    Required area = Area ABCD
                            WiredFaculty
WiredFaculty

Question
CBSEENMA12032687
Wired Faculty App

Find the area of the region bounded by y2 = x - 2, x = 4, x = 6 and the x-axis in the first quadrant.

Solution

The equation of curve is y2 = x - 2. which is right handed parabola with vertex at (2, 0).
Two lines are x = 4 and x = 6
Required area  = Area ABCD
                         WiredFaculty
WiredFaculty

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