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The area bounded by the curve y ≤ x²+3x, 0 ≤ y ≤ 4, 0 ≤ x ≤3 is

A) 59/6B) 57/4C) 59/3D) 57/6Solution: y = x2+3xy = 4 x2+3x= 4 = 0 x2+3x-4 = 0x = 1 or x = -4Area = = (1/3)+(3/2)+8= 59/6Answer: A... View Article

[latex]\int{\frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}}}.\,dx=[/latex]

A) x+2sin x+sin 2x+cB) x+2cos x+sin 2x+cC) x-2sin x+sin 2x+cD) x+2sin x-sin 2x+cSolution: = x+2 sinx+sin 2x +cAnswer: A... View Article

The line x+y = n, n∈N, makes intercepts with x²+y² = 16. Then the sum of squares of all possible intercepts

A) 105/4B) 105C) 210D) 105/2Solution:x2+y2 = 16Centre = (0,0)OA = PRadius = 4P = n/√2 To make the intercepts n/√2 < 4 n<... View Article

Let sin(α-β) = 5/13 and cos (α+β) = 3/5 where α, β ∈ (0, π/4) then tan 2α

A) 63/16B) 61/16C) 65/16D) 32/9Solution:sin(α-β) = 5/13cos (α-β) = 12/13cos(α+β) = 3/5sin(α+β) =... View Article

The sum of coefficients of even powers of x in (x+√(x³-1)⁶ + x-√(x³-1)⁶)

A) 23B) 24C) 18D) 21Solution:(x+√(x3-1)6 + x-√(x3-1)6) = 2[6C0x6 +6C2x4(x3-1)+6C4x2(x3-1)2 +6C6(x3-1)3]= 2[x6+15x4(x3-1)+15x2(x6-2x3+1)+(x3-1)3]=... View Article

∫_-π^π (cos px – sin qx)² dx where p and q are integers, then the value of the integral is

1) -π 2) 0 3) π 4) 2π Solution: (4) 2π... View Article

∫_-π/2^π/2 cos x ln [(1 + x) / (1 – x)] dx =

1) 0 2) (π2 / 4) [1 + (π / 2)] 3) 1 4) π2 / 2 Solution: (1) 0... View Article

The value of ∫_-π/4^π/4 log (sec θ – tan θ) dθ is

1) 0 2) π/4 3) π 4) π/2 Solution: (1) 0... View Article

∫₀^π/2 [sin x – cos x] / [1 + sin x cos x] dx =

1) 0 2) π/4 3) π/2 4) π Solution: (1) 0... View Article

The value of ∫₀^√2 [x²] dx, where [x] is the greatest integer function, is

1) 2 - √2 2) 2 + √2 3) √2 - 1 4) √2 - 2 Solution: (3) √2 - 1... View Article

∫₀^2π (sin x + |sin x|) dx =

1) 0 2) 4 3) 8 4) 1 Solution: (2) 4... View Article

If ∫₀²⁵ e^x-[x] dx = k (e – 1), then the value of k is

1) 12 2) 25 3) 23 4) 24 Solution: (2) 25... View Article

∫₀^π √1 + 4 sin² (x / 2) – 4 sin (x / 2) dx =

1) π - 4 2) (2π / 3) - 4 - 4√3 3) 4√3 - 4 4) 4√3 - 4 - (π / 3) Solution: (4) 4√3 - 4 - (π / 3)... View Article

The value of ∫₁^{e^2} dx / [x (1 + log x)²] is

1) 2/3 2) 1/3 3) 3/2 4) ln 2 Solution: (1) ⅔... View Article

∫₁³ [cos (log x) / x] dx =

1) 1 2) cos (log 3) 3) sin (log 3) 4) π/4 Solution: (3) sin (log 3)... View Article

∫₀^π/2 x sin x dx =

1) 0 2) 1 3) -1 4) 2 Solution: (2) 1... View Article

The value of ∫₁² dx / [x (1 + x⁴)] is

1) (1 / 4) log (17 / 32) 2) (1 / 4) log (32 / 17) 3) log (17 / 2) 4) (1 / 4) log (17 / 2) Solution: (2) (1 / 4) log (32 / 17)... View Article

The value of ∫₀¹ [√(1 – x) / (1 + x)] dx is

1) (π / 2) + 1 2) (π / 2) - 1 3) -1 4) 1 Solution: (2) (π / 2) - 1... View Article

The value of ∫₁⁴ e^√x dx is

1) e2 2) 2e2 3) 4e2 4) 3e2 Solution: (2) 2e2... View Article

The value of ∫₂³ [x + 1] / [x² (x – 1)] dx is

1) [log (16 / 9) + (1 / 6)] 2) [log (16 / 9) - (1 / 6)] 3) 2 log 2 - (1 / 6) 4) log (4 / 3) - (1 / 6) Solution: (2) [log (16 / 9) -... View Article