If f (x) = A sin ( x 2 ) + B, f^ ( 1 2 )= 2 and _ 0 ^ 1 f( x ) dx = 2 ~A then constants A…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If f (x) = A sin \(\left(\frac{\pi \mathrm{x}}{2}\right)\) + B,\(f^{\prime}\left(\frac{1}{2}\right)=\sqrt{2}\) and \(\int_{0}^{1} f(\mathrm{x}) \mathrm{dx}=\frac{2 \mathrm{~A}}{\pi}\) then constants A and B are :
- \(\frac{\pi}{2} \text { and } \frac{\pi}{2}\)
- \(\frac{2}{\pi} \text { and } \frac{3}{\pi}\)
- \(0 \text { and }-\frac{4}{\pi}\)
- \(\frac{4}{\pi} \text { and } 0\)
Answer
(D) 4 and 0
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The area of the region enclosed between the curves 7 x^ 2 +9 y+9=0 and 5 x^ 2 +9 y+27=0 is
- If I = x^ 2 + a ^ 2 x^ 4 - a ^ 2 x^ 2 + a ^ 4 ~d x then I =
- The value of the integral _ - / 2 ^ / 2 (x^ 2 + +x -x ) x d x is
- Consider the equation _ 1 ^ e ( _ e x )^ 1 / 2 x (a- ( _ e x )^ 3 / 2 )^ 2 d x=1, a (- , 0) (1, ) . Which of…
- Let f : [–1, 2] → [0, ∞ ) be a continuous function such that f ( x ) = f (1 – x ) for all x ∈ [–1, 2]. Let R_…
- _ - ^ 2 x(1+ x) 1+ ^ 2 x d x is
- For any integer n , the integral _ 0 ^ e^ ^ 2 x ^ 3 (2 n+1) x d x has the value
- If a b and a f(x)+b f ( 1 x )= 1 x -5 for all x 0 , then _ 1 ^ 2 f(x) d x= 1 a^ 2 -b^ 2 [a( 2- )+ ( b 2 ) ]…
More Integral Calculus questions · Browse all practice questions