Bihar Board Class 12 (Science) Application of Integrals — practice questions
53 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Bihar Board Class 12 (Science) Application of Integrals in the app →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?How large an area does the circle x² + y² = 49 bound? Use π = 22/7The area of the ellipse x²/16 + y²/9 = 1 equalsA plot lies under y = x² and above the x-axis between the ordinates 0 and 3. Its area isA ramp follows y = 2x + 1. How much area lies under it from x = 0 to 2?One full arch of the sine curve on [0, π] and the x-axis enclose an area ofBetween the ordinates x = 0 and x = 1, the exponential curve y = eˣ bounds an area ofUsing integration, how much ground does a circular park of radius a cover?A garden is an ellipse with semi-axes 2 m and 3 m. Its area in square metres?Quarter-disc region of radius 2 centred at the origin: what is its area?Strips drawn parallel to the x-axis give what area left of y² = 4x up to y = 3?Line y = 3x + 2 crosses the x-axis inside [-1, 1]. What total area does it cut off there?One full arch of sin x sits above the axis from 0 to π. How large is it?A right triangle lies under the line y = x up to x = 4. What area does it hold?A plot is shaped like the first quadrant of x² + y² = 9. What is its area?The area of an elementary vertical strip of height y and width dx is written as which of these?For x = g(y) between y = c and y = d, which integral gives the area?A curve has a part A1 below and a part A2 above the x-axis. What is the total area?Why is a circle's area four times the first-quadrant integral?A parabola y = x² and a chord y = x enclose a small sliver. Its area is?Sideways parabola y² = 4x and the slanted line y = x enclose a loop. Its area?A bowl-shaped curve y = x² is cut off flat by the line y = 4. Area of the cut part?Two parabolas y² = 4ax and x² = 4ay cross at the origin and again. Area between them?The U-shaped curve y = x² - 4 dips below the axis. How much area lies under the axis?A V-shaped boundary y = |x| is capped by a horizontal line at height 2. Area inside?A circular pond is modelled by x² + y² = 16. What is its area?Sideways parabola x = y² from the origin up to height 2: area against the y-axis?A triangular patch is bounded by x + y = 2 and the two coordinate axes. Its area is?An arch y = 4x - x² rises from the axis and returns to it. Area beneath the arch?What is the area of the upper half of the ellipse x²/36 + y²/4 = 1?What is a solid of revolution?Which method slices a solid of revolution perpendicular to the axis of revolution?Which method uses slices parallel to the axis of revolution?A representative disc of radius r and thickness w has what volume?Pappus's second theorem: revolved volume equals area times?