 # Banaras Hindu University (BHU) Exams Dates Released

Banaras Hindu University (BHU) Exams Dates Released The revised University entrance test schedule for admission to various Undergraduate and postgraduate courses of Banaras Hindu University has been announced. The entrance tests for all postgraduate programmes, LLB.-(3 years), B.Ed./ B.Ed. Special Education, B.P.Ed, BFA and BPA is scheduled in the first phase during August 24 to Read more about Banaras Hindu University (BHU) Exams Dates Released[…] # Inequalities – Property IV

Inequalities – Property IV Property IV: If and are integrable on the interval [a, b]. then . Proof: Let , Where , is real number. Then , , , Therefore, discriminant is non positive, i.e., , , Hence . Example: find the value of  , Solution: , , , , . Share Tweet View Email Read more about Inequalities – Property IV[…] # Inequalities – Property III

Inequalities – Property III Property: Proof: , , , , , Example: Estimate the absolute value of the integral . Solution: …(i) But , , …(ii) From equation (i) and (ii) , , , , , Therefore, the approximate value of the integral = . Share Tweet View Email Print Follow # Inequalities – Property – II

Inequalities – Property – II Property – II: If m is the value(global minimum) and M is the greatest value(global maximum) of the function f(x) on the interval [a, b] (estimation of an integral), then . Proof: It is given that . Then , It is clear from fig Area of i.e., . Share Tweet Read more about Inequalities – Property – II[…] # Inequalities – Property 1

Inequalities – Property 1 Property: If at every point x of an interval [a, b], the inequalities are fulfilled, then , where a < b. Proof: In fig. Area of curvilinear trapezoid aAFb ≤ Area of curvilinear trapezoid aBEb ≤ Area of curvilinear trapezoid aCDb i.e., Example: Prove that Solution: Hence Share Tweet View Email Read more about Inequalities – Property 1[…] # Definite Integration of Odd and Even Functions – Property II

Definite Integration of Odd and Even Functions – Property II If f(x) is an odd function, then , is an even function. Proof: , , Let t = -y dt = – dy , , As given f is an odd function , = 0 , , Hence, , is an even function. Example: Evaluate Read more about Definite Integration of Odd and Even Functions – Property II[…] # Definite Integration of Odd and Even Functions – Property 1

Definite Integration of Odd and Even Functions – Property 1 Property 1: Proof: Put x = -t in first term on R.H.S. Differentiation with respect to ‘x’ dx = – dt when x = -a x = -t -a = -t a = t and x = -t put x = 0 0 = -t Read more about Definite Integration of Odd and Even Functions – Property 1[…] # Evaluation of Trigonometric Limits

Evaluation of Trigonometric Limits (where θ is in radius) Proof: Consider a circle of radius r. let O be the center of the circle such that , where θ is measured in radians and its value is very small. Suppose the tangent at A meets OB produced at P. From fig we have Area of Read more about Evaluation of Trigonometric Limits[…] # Solution of Triangles – Part 1

Solution of Triangles – Part 1 The three sides a, b, c and the three angles A, B, C are called the elements of the triangle ABC, when any three of these six elements(except all three angles) of a triangle are given, the triangle is know as completely that is the  other three elements and Read more about Solution of Triangles – Part 1[…]