If the curve y = a√(x) + bx passes through the point (1, 2) and the area bounded by the curve, the line x = 4 , and the x-axis is 8 sq. units, then: - Mathematics MCQ Mathematics Mock Test - 6 2026 | ExamTest.live

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If the curve y = a x + b x passes through the point (1, 2) and the area bounded by the curve, the line x = 4, and the x-axis is 8 sq. units, then:

Solution & Step-by-step Explanation

1. The curve passes through (1, 2) : 2 = a 1 + b (1) ⟹ a + b = 2 \dots (i) 2. The area bounded by the curve from x = 0 to x = 4 : Area = \int_{0}^{4} (a x + b x) d x = 8 [a \frac{x ^{3/2}}{3/2} + b \frac{x ^{2}}{2}]_{0}^{4} = 8 [\frac{2 a}{3} x^{3/2} + \frac{b}{2} x^{2}]_{0}^{4} = 8 \frac{2 a}{3} (8) + \frac{b}{2} (16) = 8 ⟹ \frac{16 a}{3} + 8 b = 8 Divide by 8: \frac{2 a}{3} + b = 1 ⟹ 2 a + 3 b = 3 \dots (ii) From (i), b = 2 - a . Substitute in (ii): 2 a + 3 (2 - a) = 3 2 a + 6 - 3 a = 3 ⟹ - a = - 3 ⟹ a = 3 Then b = 2 - 3 = - 1 .

Try it yourself before checking the explanation above.

If the curve y = a x + b x passes through the point (1, 2) and the area bounded by the curve, the line x = 4, and the x-axis is 8 sq. units, then:

a = 3, b = - 1

a = 3, b = 1

a = - 3, b = 1

a = - 3, b = - 1

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