CBSE Class 12 Integral Calculus — practice questions
46 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 Integral Calculus in the app →The integral $\int x^3\, dx$ equals:The definite integral $\int_0^1 x\, dx$ equals:To evaluate $\int x\cos x\, dx$, the best technique is:If $f$ is an odd function, $\int_{-a}^a f(x)\, dx$ equals:Formulae of elementary geometry cannot find areas enclosed by:The area under a curve is built from a large number of thin:For a vertical strip of height y and width dx, dA equals:The area of one thin strip is called the:The total area comes from adding up all the:The definite integral is evaluated using which theorem?Strips used to find an area may be vertical or:If a curve lies below the x-axis, its integral comes out:When the integral is negative, the area is taken as its:If part of a curve is above the axis and part below, the areas are:For the region below the axis A1 is negative while A2 is:For a horizontal strip, the elementary area would be:Areas are found here for lines and arcs of circles, plus:The width of an elementary vertical strip is written as:The definite integral was first defined as the limit of:The height of a vertical elementary strip is given by:An elementary area is located at a position specified by some value of:Only the numerical value of an area is taken into consideration, so signs are:Finding the area of a circle here uses which curves in standard form?Slicing a region the other way is described in the text as considering:For different values of C, the integrals of 2x form a family of:The parabolas in that family all have their axis along the:For C equal to zero, the parabola has its vertex at the:Members of the family of curves are obtained from one another by shifting:Two indefinite integrals with the same derivative lead to the same:Which is one of the methods of integration studied?Integration by partial fractions applies to a ratio of two:A rational function is defined as the ratio of two:Integration by parts is described as useful for integrating:How many named methods of integration are introduced after inspection?The definite integral can be introduced as the limit of a:If F is an anti derivative, the definite integral equals F at the end points taken as a:For the limit of a sum, the function f must be:The definite integral is taken over an interval that is:The Fundamental Theorem of Calculus is introduced through a function called the:The two ways of introducing the definite integral are limit of a sum and:Indefinite integrals were studied before the section on integrals that are:The geometrical interpretation of an indefinite integral is a family of:Shifting the parabola y equals x squared one unit up gives the member with C equal to:For a negative value of C, the parabola's vertex lies on the y-axis on the side that is:In integration by substitution, the aim is to rewrite the integrand in a form that is:The definite integral of f from a to b is a: