EXERCISE 1
A) ∫ f⁻¹(y) dy at (f(b), f(a))
B) ∫ f⁻¹(y) dy at (b, a)
C) ∫ f(x) dx at (b, a)
D) ∫ f(x) dx at (f(b), f(a))
2) The area bounded by the lines y=|x - 2|, |x| = 3 and y= 0 is
A) 13unit² B) 5 unit² C) 9 unit² D) 7 unit²
3) The area bounded by the curve y= √(4- x²) and the line y= 0 is
A) 4π. B) 2π. C) π. D) π/2
4) The area bounded by the curve y² = 4x and the double ordinate x= 2, is
A) 4√2/3 unit² B) 8√2/3 unit² C) 16√2/3 unit² D) 30√2/3unit²
5) The area bounded by the curve x² = ky, k > 0 and the line y= 3 is 12 unit². Then k is
A) 3 B) 3√3 C) 3/4 D) none
6) The area bounded by the curve y= 2ˣ , the x-axis and the y-axis.
A) logₑ2 B) log ₑ4 C) log₄e D) log ₂e
7) The area of the portion enclosed by the curve √x +√y = √a and the axes of reference is
A) a²/6 B) a² C) a²/2 D) a²/4
8) The area bounded by the curve x= cos cos⁻¹y and the lines | x|= 1 is
A) sin 1 B) cos 1 C) 2 sin 1 D) 2cos 1
9) The area of bounded by the curve y=√x, the line 2y +3= x and the x-axis in the first quadrant is
A) 9 B) 27/4 C) 36 D) 18
10) the area of the region bounded by the pair of lines y=|x -1| and y= 3 - |x| is
A) 3 unit² B) 4 unit² C) 6unit² D) 2 unit²
11) The ratio in which the area bounded by the curves y² = 4x and x²= 4y is divided by the line x= 1 is
A) 64: 49 B) 15: 34 C) 15:49 D) n
12) Let f(x) be a continuous function such that the area bounded by the curves y= f(x), the x-axis and the two ordinates x= 0 and x= a is a²/2 + a/2 sin a + π/2 cos a. Then f(π/2) is
A) 1/2 B) π²/8 +π/4 C) (π+1)/2 D) π/2
13) the area bounded by the curve f(x)= ceˣ (c> 0), the x-axis and the two ordinates x = p and x= q is proportional to
A) f(p).f(q) B) |f(p) - f(q)| C) f(p) + f(q) D) √f(p). f(q)
14) The ordinate x= a divides the area bounded by the x-axis, the curve y= 1 + 8/x² and the ordinats x= 2 and x= 4 into equal parts. Then a is.
A) 3 B) 7/2 C) 2√2 D) 5/2
15) The area of the ellipse (x+1)²/4 + y²= 1 falling in the first quadrant is
A) (4π - 3√3)/6 B) (4π - 3√3)/12 C) √3/2. D) (π - √3)/3
ANSWERS
1) C 2) A 3) B 4) C 5) A 6) D 7) A 8) C 9) A 10) B 11) C 12) A 13) B 14) C 15) B
EXERCISE -2
1) The area enclosed by the curve y= x², the straight line y= x +2 and the x-axis is
A) 5/6 sq. unit B) 5/4sq. unit C) 5/2 sq. unit D) none
2) The area bounded by the curve y²+ 6x= 0 and y² + 4x= 4 is
A) 4/√3 sq. unit B) 8/√3 sq. unit C) 4√3 sq. unit D) none
3) The area bounded by y= |x -1|, |x|= 2 and the x-axis is
A) 3 sq. unit B) 4 sq. unit C) 5 sq. unit D) none
4) The area bounded by the lines |x|+|y|= 1 is
A) 15sq. unit B) 2sq. unit C) 3sq. unit D) 4sq. unit
5) The area bounded by y=|x|, |x|= 1and the x-axis is
A) 1sq. unit B) 2sq. unit C) 3sq. unit D) 4 sq. unit
6) The area bounded by y=|x -1| and y= 1 is
A) 1/2sq. unit B) 1 sq. unit C) 2sq. unit D) 4 sq. unit
7) The area bounded by y= 1 - |x| and the x-axis is
A) 1/3sq. unit B) 1/2 sq. unit C) 1 sq. unit D) 2sq. unit
8) The area bounded by y = |sinx|, the x-axis and the lines |x| =π/2 is
A) 1 sq. unit B) 1/2 sq. unit C) 2 sq. unit D) none
9) The area bounded by the lines y= |x -1| and y= 3 - |x| is
A) 1 sq. unit B) 2 sq. unit C) 3 sq. unit D) 4 sq. unit
10) The area included between y=√(8- x²) and y=|x| is equals to
A) π sq.unit B) 3π/2 sq unit C) 2π sq unit D) 3/2 (π +1) sq unit
11) The smaller area included between x²+ y²= a² and the line x+y = a is
A) a²/4 (π -2) sq. unit B) a²/4 (2 - π)sq. unit C) a²/4 (π +2) sq. unit D) none
12) The smaller area included between y=√(4 - x²), y= x √3 and the x-axis is
A) π/3 sq. unit B) 2π/3 sq. unit C) 4π/3 sq. unit D) none
13) The area included between x² + y²= 2ax and y²= ax is
A) a²/8 (3π - 8) sq. unit B) a²/6 (3π +8)sq. unit C) a²/6 (3π -8) sq. unit D) none
14) The area included between y²= 4x and x²= 4y is
A) 20/3 sq. unit B) 32/3 sq. unit C) 16/3 sq. unit D) none
15) The area bounded by y= x², y= 0, x= 2, x= 4 is.
A) 6 sq. unit B) 12 sq. unit C) 53/3 sq. unit D) 56 sq unit
16) T area bounded by a²= 4x, x= 0, and y= 2 is
A) 3/2 sq. unit B) 2/3 sq. unit C) 3 sq. unit D) none
17) The area bounded by y= x² and y= x³ is
A) 1/12 sq. unit B) 1/6 sq. unit C) 1/24 sq. unit D) none
18) The area bounded by the parabola the y²= 4a(x +a) and y²= -4(x - a), a > 0, is
A) 16a²/3 sq. unit B) 8a²/3 sq. unit C) 4a²/3 sq. unit D) none
19) The area of the region bounded by y= |[x - 1]|, the x-axis and the lines x =|2|
A) 6 sq. unit B) 8 sq. unit C) 4 sq. unit D) none
Answers
1) A 2) B 3) C 4) B 5) A 6) B 7) C 8) C 9) D 10) C 11) A 12) B 13) C 14) C 15) D 16) B 17) A 18) A 19) D
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