Let √(x)√(1-x^3) dx = 2/3 (g f)(x) + c . Then: - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

mediumMCQMathematics Mock Test - 112026Mathematics

1 mark

Let \int \frac{x}{1 - x ^{3}} d x = \frac{2}{3} (g \circ f) (x) + c . Then:

Solution & Step-by-step Explanation

I = \int \frac{x}{1 - ( x ^{3/2} ) ^{2}} d x .Let t = x^{3/2} ⟹ d t = \frac{3}{2} x^{1/2} d x ⟹ x d x = \frac{2}{3} d t . I = \int \frac{2/3}{1 - t ^{2}} d t = \frac{2}{3} sin^{- 1} t + c I = \frac{2}{3} sin^{- 1} (x^{3/2}) + c .Comparing with \frac{2}{3} (g \circ f) (x) + c : g (x) = sin^{- 1} x and f (x) = x^{3/2} .Option B is the correct match for f (x) .

Try it yourself before checking the explanation above.

Let \int \frac{x}{1 - x ^{3}} d x = \frac{2}{3} (g \circ f) (x) + c . Then:

f (x) = x

f (x) = x^{3/2}

g (x) = sin x

g (x) = sin \frac{x}{3}

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