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jee_main_2024_30_january_evening - Integral Calculus Topics

Master these core formulas and structures to solve almost any past paper question.

Sample Questions in this Chapter

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 fracpi6 and fracpi4 , respectively with positive x-axis. If 27int_1^3left(left(f'(t)right)^2 + 1right)f''(t)dt = alpha + beta sqrt3 quad textwhere alpha, beta text are integers, then the value of alpha +beta text equals
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QUESTION #12 Definite Integration
Let f:mathbbR to mathbbR be defined f(x) = ae^2x + be^x + cx . If f(0) = -1 , f'(log_e 2) = 21 and int_0^log_e 4 (f(x) - cx) dx = frac392 , then the value of |a + b + c| equals :
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QUESTION #19 Definite Integration
Let f:mathbbR to mathbbR be a function defined f(x) = fracx(1 + x^4)^1/4 and g(x) = f(f(f(f(x)))). Then 18int_0^sqrt2sqrt5 x^2 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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