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Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Concept: Area Under Simple Curves
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5.
Concept: Standard Forms of Parabola and Their Shapes
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
Concept: Area Under Simple Curves
The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`
Concept: Area Under Simple Curves
Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3
Concept: Area Under Simple Curves
Find the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3
Concept: Area Under Simple Curves
Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5
Concept: Area Under Simple Curves
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
Concept: Area Under Simple Curves
The area of the region bounded by the curve y = x2, x = 0, x = 3, and the X-axis is ______.
Concept: Area Under Simple Curves
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
Concept: Area Under Simple Curves
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
Concept: Area Under Simple Curves
Determine the order and degree of the following differential equation:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Concept: Order and Degree of a Differential Equation
Determine the order and degree of the following differential equation:
`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`
Concept: Order and Degree of a Differential Equation
Solve the following differential equation:
`x * dy/dx - y + x * sin(y/x) = 0`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Homogeneous Differential Equations
Solve the following differential equation:
`x^2 dy/dx = x^2 + xy + y^2`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Homogeneous Differential Equations
Solve the following differential equation:
(x2 – y2)dx + 2xy dy = 0
Concept: Methods of Solving First Order, First Degree Differential Equations >> Homogeneous Differential Equations
Solve the following differential equation:
`dy/dx + y/x = x^3 - 3`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
Solve the following differential equation:
`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
Solve the following differential equation:
dr + (2r cotθ + sin2θ)dθ = 0
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.
Concept: Application of Differential Equations
