$$Evaluate\;\int_0^x {\cos t} dt =$$

• A) $$\sin t$$
• B) $${\cos x}$$
• C) $$\sin x$$
• D) $${\cos t}$$

What is the relationship between the area under a curve and the definite integral?

• A) They are unrelated concepts.
• B) The area is the antiderivative of the integral
• C) Both are same concepts.
• D) The area is the derivative of the integral.

$$If\,f(x)\, = \,x^2 ,\,\,then\,\,\int\limits_0^2 {\pi \,[f(x)} ]^2 \,dx\,\,is\,\, - - - - - - -$$

• A) $$\frac{{32\pi }} {5}$$
• B) $$\frac{{17\pi }} {5}$$
• C) $$\frac{{23\pi }} {5}$$
• D) $$\frac{{7\pi }} {5}$$

Which of the following statements is true about $\int\limits_0^1 {(\sin x + \cos x )dx}$?

• A) $$\int\limits_0^1 {(\sin x + \cos x )dx} = [\cos x ]_0^1 + [\sin x ]_0^1$$
• B) $$\int\limits_0^1 {(\sin x + \cos x )dx} = [\sin x]_0^1 - [\cos x]_0^1$$
• C) $$\int\limits_0^1 {(\sin x + \cos x )dx} = - [\sin x]_0^1 + [\cos x]_0^1$$
• D) None

The volume of a cylinder is the area of a cross section of the cylinder multiplied by the ________ of the cylinder.

• A) Diameter
• B) Radius
• C) Base
• D) Height

If we change the letter for the variable of integration but don’t change the limits, then the values of the definite integral will be …………

• A) Changed
• B) Unchanged
• C)
• D)

The value of $\int\limits_0^1 {\frac{{dx}}{{1 + {x^2}}}} \,\_\_\_\_\_.$

• A) $$\frac{\pi }{2}$$
• B) 0
• C) $$\frac{\pi }{4}$$
• D) $$\infty$$

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• A) data:image/png;base64,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.
• B) data:image/png;base64,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.
• C) data:image/png;base64,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.
• D) data:image/png;base64,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.

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• A) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI4AAAAXCAYAAADdlHeDAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAKzSURBVGhD7ZaLreIwEEXphWKohVKohEKog1qyOk+c1X0jJ9n1orBPmiNZiT2ej8eXiNPSNBO0cJopWjjNFC2cZooWTjPFN+HcbrfldDr9Hufz+WU5lvv9/pX/aK7X63K5XF6z/x96xJ2tsWf/F4a3Q0Iu7xMomqOFg2jI+ZOEs4U9/LhwjmzoUV8cmvp4PF6zn/fF2ePjwjnqIuWIfM/n8ytHC2eOXeGQmLmD5o7Qx08+A9I/xciFuc7IC6vCyX2ScfO/mIJgkGPUuJpbf4WT9uqPXVv2gn3Eyfz6Ol/7z5j57INzBjFzjf3myZ7W3D6lntu4kD7VNmJXOFAvsmKy9HNu4TQ5G8e7Ng/EEzIf7/UrgF82BLt7eHrozFGxyeYERW8sfLNm1nO/52PwznB/roH5sq8V7BmffFWcxDFWxqvnMT9PYN1zgXYwVp51j7cIB6rP6NCjwozN8NCu4ZMxhDj65ADyZoPWWBNO+ua587JyuL+ej7jY8RPm2aNK7RlzfEQRgPUYD7/aK+z6YGNeh+fnfau2yseEY0z21EvU5qiwlheSeGGOtX01J1DLmnDYt/WLfIdwMh9+znky3xJO7Tdg1wf7Vu692iofEU69tDrPfMTJywTi7B3SmMap1JywJRz38xzxDuGAe+ydNbGWsazHeKM+YVc4xMn7qPxJbclfCydVn1QfDpGFjoTjfuOPhAO811isZSO1k9d184zQRs5sbja/1oEtxQHmzfPBrHCIx7Am41RRWH/tYZ0ziGWczM+7Pa+2Pb511Qtx1ItmmEjSxrCBzhVQ7oFcy/f0ZdT4Hq7GdL3mr/Um7sOHOvVhvfZCAYzqG9WyNSf2Gu41H1iPrPUka7am9Kt1sKfGcr/+WUcy/jk2zQ4tnGaKFk4zRQunmaKF00zRwmmmaOE0EyzLL7YhRyXTWTekAAAAAElFTkSuQmCC.
• B) data:image/png;base64,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.
• C) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAAAdCAYAAADckDwLAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAOYSURBVHhe7ZcNjcJAEIWxgAYs4AEJaMACDnCAAxSgAAMYwAEeevnIveRlMgUaetDl5ks2Zf9mZ2Zft8usK4pGKfEWzVLiLZqlxFs0S4m3aJYSb9EsJd6iWUq8RbOUeItmKfEWzfJx8R4Oh242m3Wr1eq35Xmu12u3Xq9v8yljcz6fu/l8/ie2P8Vms7nFs9vtflvaZfCuLBaLW/BsKps7Btvt9qF46Y9jqLMJiBi//oLj8Th58Q4V43K5/J/iPZ1Ot2TxFJfL5aUNJpFDxYtgox+c4o/s3CObr3inzFDxEuOj8RwGntspMop4Xz2dnhFvJPPjmRP8Htl8rfNNPBJvdjBMkZfFy2mle6FKlhiuGH4/5c3WtUPipa5rCXWSCPFe7ONUEJ7XKfiIDe558pEn9iJ98xUvdlif3+67IAb5xGdZ/Ty1Nr9lQ/Exj/4+v8Dj99jxLbvD+jpeaAOejPe9I35w+3He1Bjl5FXbPRAuBdg0Nlg2tPFKoE5ynoIEehIzP7ATE73f72+29SKw2b7RTjZf6zAPG1yR2HD5ChIBGw/0sabALjZoxwbjqLOW/Oc3OemDfuWIvLCe5mLLY2Ic/gL+em5Ba+lloQ8byhFQ99xOkbeK1wXrkPi4cXFDSDhFZH5k4kO89041J5uvdXxjoy/47uLQfwCJGbsxPzG+bIzDen3ijrao38sLv93fLJexPkXeJl42X584TgI/VWNygXG+IfT7mMyPzA7QjoApbjOSzc9ii77QnxX5hl3qDnX3JRvjxDWdaIv8cliQc4qfxIAdH5/lMtanyNvEK0gmpyHj/WSKG0O/JzhuXuZHZsfR55b1M7L5WWzRF8ThvkboizZifNkYJ67pRFv4TJy0U3TlEdiJ4xnnuYz1KTKqeHkiSP8kCZIpserOJxuMH+vawDpsFNcECnN0ZdAp5HadbL7u33Hz3RfNky/Ep/s90I8NJ8aXjXHimk601Xc9E/Gak+VSNolbsdDW58MnGCxeNp8gXIxAUArON1qoX3OVPASidn3aSJbGsYaP0amZ+aE/J7TLPk/GaL4+pxlxPnY1l3bQV4PiLwW+ayyxyie3IRHo+kShn6K6f95FliMRbYHnWgXBEp+Pl/8xRtDLRJvsUsf2VBgs3mLaIDSE6i8ov2nz0/kbKPF+GQjUT0vgOkCbTtpvocT7ZcQrDIVTt+9PasuUeItmKfEWzVLiLZqlxFs0S4m3aJSu+wGH0JC5n5D+KgAAAABJRU5ErkJggg==.
• D) data:image/png;base64,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.

Which of the following is the value of definite integral of f(x)=(x-1), where the lower limit is 0 and upper limit is -1?

• A) 2/3
• B) 0
• C) 1
• D) 3/2

Definite integral can be…………..

• A) Negative
• B) 0
• C) All of these
• D) Positive

Which of the following is the definite integral of f(x) =x^2 from x=1 to x=2

• A) None of these.
• B) 8/3
• C) 7
• D) 7/3

If the definite integral of f(x)= sec2 x over the interval [0, a] is equal to ‘1’ then what will be the value of the definite integral of f(x)= (sec2 x) +3 over the same interval?

• A) -1-3a
• B) 1+3a
• C) 1-3a
• D) 4

For a function f(x) that is decreasing on the interval [a, b], how would this affect the volume of the solid of revolution?

• A) Cannot be determined.
• B) Volume decreases.
• C) No effect on volume.
• D) Volume increases.

$$If\;\;m \leqslant f(x) \leqslant M\;for\;any\;two\;number\;such\;that\;,a \leqslant x \leqslant b,\;which\;of\;the\;following\;is\;true$$

• A) $$m(b - a) \geqslant \int_a^b {f(x)} dx \geqslant M(b - a)$$
• B) none of these
• C) $$m(b - a) \leqslant \int_a^b {f(x)} dx \leqslant M(b - a)$$
• D) $$m(b - a) \geqslant \int_a^b {f(x)} dx \leqslant M(b - a)$$

Antiderivative of f(x)=x^2 is ...........

• A) None of these.
• B) (1/3) x^3+c
• C) x^3
• D) x/2

Which of the following statements is true?

• A) None
• B) An antiderivative of a difference is the difference of the antiderivatives.
• C) A constant factor can be moved through an integral sign only if the constant is positive.
• D) An antiderivative of a sum is the sum of the twice of antiderivatives.

The value of $\int\limits_0^{\frac{\pi }{6}} {\sin x\cos x\,dx} \,\_\_\_\_\_\_\_.$

• A) $$8$$
• B) $$4$$
• C) $$\frac{1}{8}$$
• D) $$\frac{1}{4}$$

The value of definite integral of a function f(x) taken from 7 to 7 is 0.

• A) False
• B) True
• C)
• D)

The anti-differentiation of a function and integration of a function are two different things.

• A) True
• B) False
• C)
• D)