The value of the definite integra equal to a.
Let a, b, c be nonzero real numbers such that
Then the quadratic equation ax^{2} + bx +c= 0 has
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The area bounded by the curves y = f(x), the xaxis and the ordinates x = 1 and x = b is (b – 1) sin (3b + 4). Then f(x) is
The value of the integral
For any integer n the integral ––
has the value
Let f : R → R and g : R → R be continous functions. Then the value of the integral
The value of
If f (x) and then constants A and B are
The value of represents the greatest integer function is
equals
If for a real number y, [y] is the greatest integer less than or equal to y, then the value of the integral
where f is such that
Then g(2) satisfies the inequality
The value of the integral
The value of
The area bounded by the curves y = x –1 and y = –x + 1 is
Then the real roots of the equation x^{2} – f '(x) = 0 are
Let T > 0 be a fixed real number. Suppose f is a continuous function such that for all
The integral
then the expression for l(m, n) in terms of l(m + 1, n – 1) is
increases in
The area bounded by the curves and xaxis in the 1^{st} quadrant is
If f (x) is differentiable and equals
The value of the integral
The area enclosed between the curves y = ax^{2} and x = ay^{2} (a > 0) is 1 sq. unit, then the value of a is
Th e area bounded by the par abolas y = (x + 1)^{2} and y = (x – 1)^{2} and the line y = 1/4 is
The area of the region between the curves and bounded by the lines x = 0 and is
Let f be a nonnegative function defined on the interval
and f (0) = 0, then
The value of
Let f be a realvalued function defined on the interval (–1, 1) such that and let f ^{–1} be the inverse function of f. Then (f –1)' (2) is equal to
The value of
Let the straight lin e x = b divide the area enclosed by y = (1 – x)^{2} , y = 0, and x = 0 into two parts R_{1} (0 < x < b) and R_{2} (b < x < 1) such that R_{1}  R_{2} = 1/4. Then b equals
Let f : [– 1, 2] → [0, ∞) be a continuous function such that f (x) = f (1 – x) for all x ∈ [–1, 2]
and R_{2} be the area of the region bounded by y = f (x), x = –1, x = 2, and the xaxis.
Then
The value of the integral
The area enclosed by the curves y = sin x + cos x and y = cosx  sinx over the interval
(the set of all real number) be a positive, nonconstant and differentiable function such that Then the value of in the interval
The following integral
The value of is equal to
Area of the region is equal to
447 docs930 tests

Test: Area Between A Curve And A Line Test  10 ques 
Test: Application of Integrals 1 Test  25 ques 
Test: Application of Integrals 2 Test  25 ques 
JEE Advanced Level Test: Area Under Curve With Solution Test  30 ques 
JEE Advanced (Subjective Type Questions): Definite Integrals & Applications of Integrals  2 Doc  8 pages 
447 docs930 tests

Test: Area Between A Curve And A Line Test  10 ques 
Test: Application of Integrals 1 Test  25 ques 
Test: Application of Integrals 2 Test  25 ques 
JEE Advanced Level Test: Area Under Curve With Solution Test  30 ques 
JEE Advanced (Subjective Type Questions): Definite Integrals & Applications of Integrals  2 Doc  8 pages 