jee_main_2024_30_january_evening - Integral Calculus Topics

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QUESTION #9 Definite Integration
Let y = f(x) be a thrice differentiable function in (-5, 5) . Let the tangents to the curve y = f(x) at (1, f(1)) and (3, f(3)) make angles (π)/(6) and (π)/(4) , respectively with positive x-axis. If 27∫₁³((f'(t))² + 1)f''(t)dt = α + β √(3) where α, β are integers, then the value of α +β equals
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QUESTION #12 Definite Integration
Let f: R → R be defined f(x) = ae2x + be^x + cx . If f(0) = -1 , f'( ₑ 2) = 21 and ∫₀ₑ 4 (f(x) - cx) dx = (39)/(2) , then the value of |a + b + c| equals :
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QUESTION #19 Definite Integration
Let f: R → R be a function defined f(x) = x(1 + x⁴)1/4 and g(x) = f(f(f(f(x)))). Then 18∫₀^ 2√(5) x² g(x) dx is
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QUESTION #29 Area Under Curve
The area of the region enclosed by the parabola (y - 2)² = x - 1 , the line x - 2y + 4 = 0 and the positive coordinate axes is
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Rankbit System
JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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