alleryStart learning →The parabola y² = 4x is cut off by the vertical line x = 1; the enclosed area is
- 8/3
- 4
- 16/3
- 4/3
Show answer and solution
Correct answer: A. 8/3
Twice the integral of 2√x from 0 to 1 is 2 × 4/3 = 8/3.
MHT-CET Application of Definite Integration — practice questions — page 2
Explore 47 free Application of Definite Integration questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–47 of 47.
The parabola y² = 4x is cut off by the vertical line x = 1; the enclosed area isRead the answer and worked solution →A triangular region lies under the line y = 3x for x between 0 and 2; its area isRead the answer and worked solution →Beneath y = √x, the strip between x = 1 and x = 4 has what area?Read the answer and worked solution →The curve y = eˣ with the X-axis over [0, 2] bounds an area ofRead the answer and worked solution →The decaying curve y = e⁻ˣ and the X-axis over 0 ≤ x ≤ 1 encloseRead the answer and worked solution →Compute the area of the strip below y = 1/x² standing over [1, 2].Read the answer and worked solution →Find the area under the tangent curve y = tan x for x from 0 to π/4.Read the answer and worked solution →Since tan x differentiates to sec² x, the area under sec² x on [0, π/4] isRead the answer and worked solution →Integrating 1/(1 + x²) over the interval from 0 to 1 gives an area ofRead the answer and worked solution →If f(x) ≥ g(x) on [a, b], the area between the curves is the integral ofRead the answer and worked solution →Which integral gives the area enclosed by x = g(y), the Y-axis, y = c and y = d?Read the answer and worked solution →By symmetry, an ellipse has an area equal to how many times its first-quadrant area?Read the answer and worked solution →If ∫f(x)dx = φ(x), the area under f from x = a to b (f ≥ 0) isRead the answer and worked solution →The parabolas y² = 4x and x² = 4y intersect at the pointsRead the answer and worked solution →Because x² is even, its area from −1 to 1 is double that over [0, 1], namelyRead the answer and worked solution →Integrating in y, the area between x = y², the Y-axis and y from 0 to 2 isRead the answer and worked solution →The area between y² = 4ax and its latus rectum isRead the answer and worked solution →
Worked practice questions
A triangular region lies under the line y = 3x for x between 0 and 2; its area is
- 12
- 3
- 6
- 9
Show answer and solution
Correct answer: C. 6
Area = [3x²/2] from 0 to 2 = 6.
Beneath y = √x, the strip between x = 1 and x = 4 has what area?
- 7/3
- 3
- 28/3
- 14/3
Show answer and solution
Correct answer: D. 14/3
Area = (2/3)(8 − 1) = 14/3.
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