∫sin-1 (cos 3x) dx =
1) (3π / 2) x – (x2 / 2) + c 2) (π / 2) x – (3x2 / 2)... View Article
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If f (x) and g (x) are twice differentiable function on (0, 3) satisfying f ” (x) = g” (x), f ‘ (1) = 4, g’ (1) = 6, f (2) = 3, g (2) = 9, then f (1) – g (1) is equal to
1) 4 2) – 4 3) 0 4) – 2 Solution: (2) – 4 f ” (x) = g” (x)... View Article
If I1 = ∫sin-1 x dx and I2 = ∫sin-1 √(1 – x2) dx, then
1) I1 = I2 2) I2 = π / 2 I1 3) I1 + I2 = (π / 2) x... View Article
∫1 / (√7 – x2) dx =
1) (1 / 2√7) log |(√7 + x) / (√7 – x)| + C 2) sin-1 (x / √7) +... View Article
The value of ∫(cos 2x – 1) / (cos 2x + 1) dx is
1) tan x – x + C 2) tan x + x + C 3) x – tan x +... View Article
∫ax dx =
1) (ax / x loge a) + c 2) ax loge a + c 3) (ax / loge a) +... View Article
If ∫(x2 – 1) / [(x + 1)2 √[x (x2 + x + 1)]] dx = A tan-1 [(√x2 + x + 1) / (x)] + c where c is real constant, then A =
1) 1/2 2) 3 3) 2 4) 1 Solution: (3) 2 \(\begin{array}{l}\begin{array}{l} \int \frac{\left(x^{2}-1\right) d x}{(x+1)^{2} \sqrt{x\left(x^{2}+x+1\right)}}=\operatorname{Atan}^{-1}\left(\sqrt{\frac{x^{2}+x+1}{x}}\right)+C \\ \frac{d}{d x}... View Article
If ∫dx / [(1 + √x) (√x – x2)] = (A √x / (√1 – x)) + B / (√1 – x) + c where c is real constant, then A + B =
1) 3 2) 0 3) 1 4) 2 Solution: (2) 0 \(\begin{array}{l}\int \frac{d x}{1+\sqrt{x} \sqrt{x-x^{2}}}=\frac{A \sqrt{x}}{\sqrt{1-x}}+\frac{B}{\sqrt{1-x}}+C\\ \text {Differentiating both the... View Article
∫√(1 + cos x) dx =
1) 2 sin (x / 2) + c 2) √2 sin (x / 2) + c 3) (1 / 2)... View Article
∫dx / (sin x – cos x + √2) =
1) (- 1 / √2) tan [(x / 2) + (π / 8)] + c 2) (1 / √2) tan... View Article
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